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  1. schoen yau lectures on differential geometry



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Beginning in Spring 2020, the CMSA will be hosting a lecture series on ... January 13 , 2021 | 9:00 – 10:30am ET ... in some sense not really a branch of topology at all, but of differential geometry. ... a duality between families of Calabi​-Yau varieties acting as a mirror reflection on the Hodge diamond. ... Abstract PDF | Video

  1. schoen yau lectures on differential geometry

by L Ji · 2010 — 13. Solution to the positive mass conjecture in general relativity (1979-1981) ... [​94-8] R. Schoen, S.T. Yau, Lectures on differential geometry, .... Schoen/Yau, Lectures on Differential Geometry (1994). (Heavyweight lifting.) ... PDF (www.caressa.it): A high-quality OCR scan of the original Latin DG paper (​37 pages). ... Volumes 1, 3 and 4 are currently (2013-7-13) available at archive.​org.. by ST Yau · 2006 · Cited by 11 — I dedicate the lecture to the memory of my teacher S. S. Chern who had ... international conferences on differential geometry and differential ... 2.3. Functions and tensors defined by linear differential equations. 13. 3. ... There was also the work of Schoen-Wolpert-Yau [591] on the behavior of eigenvalues.

schoen yau lectures on differential geometry

schoen yau lectures on differential geometry, schoen yau lectures on differential geometry pdf

by D Huybrechts · Cited by 428 — 13. For a locally free sheaf (or an arbitrary coherent) sheaf F on a K3 surface X the ... geometry of K3 surfaces shows surprising analogies to the theory of linear systems on ... the differential of arbitrary variations of Hodge structures. ... His argument relies on the proof of Calabi's conjecture by Yau and previous work.

PDF | These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. ... toric geometry such as [23, 13, 12]. ... form, which is a complex-valued differential form with pholomorphic pieces and qanti- ... These threefolds arise as quotients of Schoen's Calabi-Yau threefolds, which are fiber .... Grigor'yan, A., Sun Yuhua, "Analysis and partial differential equations on manifolds ... Grigor'yan, A., Lin Yong., Yau S.-T., Torsion of digraphs and path complexes, preprint, ... analysis on manifolds with ends, Advances in Analysis and Geometry 3, 325-344 (pdf) ... L. Ji, P. Li, R. Schoen, L. Simon, Advanced Lectures in Math.. 13. Covariant derivatives and curvature on general vector bundles. 14. ... These are notes for a course in differential geometry, for students who had a ... Schoen and Yau [SY] obtained topological consequences, for a compact, oriented.

Cambridge Core - Geometry and Topology - Geometric Analysis. ... Subjects: Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical ... PDF; Export citation ... 13 - Upper and lower bounds for the heat kernel ... [SY2] R., Schoen and S. T., Yau, Lectures on differential geometry, Conference .... by Lizhen Ji, Kefeng Liu, Lo Yang, and Shing-Tung Yau (Ed.), HEP & IP, 2008. Handbook of Geometric Analysis Vol. I by Lizhen Ji, Peter Li, Richard Schoen, .... by R SCHOEN · Cited by 1264 — ... SCHOEN. A well-known open question in differential geometry is the question of ... hand, it is a theorem of the author and S. T. Yau that A > 0 and A = 0 only if.. by X Dai · Cited by 7 — Ricci tensor and Ricci flow in the rest of lectures. ... 2 Geometry of Manifolds with Ricci Curvature Lower Bound. 27 ... Theorem 1.4.13 (Cheng's Maximal Diameter Theorem 1975) Suppose Mn has RicM ... Then its differential is given in terms of Jacobi fields. ... Schoen-Yau [115] proved that any complete.. Jun 28, 2021 — Furthermore, the second part of the book (chapters 13–18) can be used as a ... Lectures on differential geometry yau schoen pdf download .... Feb 26, 2020 — Richard Schoen (Stanford University). Shing-Tung Yau (Harvard University) .... This book, Lectures on Differential Geometry, by Schoen and Yau, .... by FC Marques — The content of the paper essentially appeared on a lecture given by the ... XIII Brazilian School of Differential Geometry, held at IME-USP in 2004. Due ... Trudinger ([33]), Aubin ([1]) and Schoen ([30]), the Yamabe problem was fi- nally given an ... of manifolds, for example it has been conjectured by S. T. Yau (see Chapter.. by R SCHOEN · 2017 — These are notes from Rick Schoen's topics in differential geometry course taught at ... 286 - TOPICS IN DIFFERENTIAL GEOMETRY - LECTURE NOTES. 13. = ∂. ∂z ... Suppose Σn ⊂ M2n is Lagrangian submanifold in a Calabi-Yau manifold.. Richard Schoen is part of Stanford Profiles, official site for faculty, postdocs, students and staff information (Expertise, ... Editor, Journal of Differential Geometry.. by J Lafferty · 2005 · Cited by 294 — The Laplacian on a Riemannian Manifold. Cambridge University Press, 1997. Richard Schoen and Shing-Tung Yau. Lectures on Differential Geometry, volume 1 .... This volume presents lectures given by Richard Schoen and Shing-Tung Yau at the Institute for Advanced Studies at Princeton University in 1984 and 1985.. The pdf file of the lectures can be found on duo (under other resources). ... Jeffrey lee, manifolds and differential geometry, chapters 12 and 13 - center ... Lectures on differential geometry (2010 re-issue) schoen, richard; yau, shing-tung.. by M del Mar GONZALEZ — Key Words: σk–curvature, fully nonlinear elliptic equations, conformal geometry, singular metrics. AMS subject classification: 35J75, 53C21, 58J60.. Differential Geometry Course : Syllabus, Notes on geodesic convexity ... Luminy Lecture on Tangents, Densities, and Riesz Characteristics ... 73 (2001), 145-160, available in pdf file 13. (with F. Reese Harvey and J. Zweck) "The de ... Surveys in Differential Geometry, edited by H.-D. Cao, J. Li, R. Schoen and S.-T. Yau, vol.. by M Lesourd · 2021 — Lectures on Differential Geometry. International Press, 1994. [37] Schoen, R., and Yau, S.-T. Positive scalar curvature and minimal.. [13] K. Uhlenbeck: “Generic properties of eigenfunctions,” Am. J. Math. ... 455–​​464 in Seminar on differential geometry. ... [23] R. Schoen and K. Uhlenbeck: “A regularity theory for harmonic maps,” J. Diff. Geom. ... Lecture Notes in Mathematics 949. ... [37] K. Uhlenbeck and S. T. Yau: “A note on our previous paper: On the .... Schoen, r: lectures on differential geometry schoen, richard, yau, shing- tung isbn​: ... Pdf on jan 1, 2005, ivan avramidi published lecture notes introduction to differential ... 13 may 2019 i stumbled upon a good series on riemannian geometry, .. Sep 21, 2020 — Schoen Yau Lectures On Differential Geometry Pdf 13l ##BEST##. schoen yau lectures on differential geometry, richard schoen and shing-tung .... by Z Djadli · Cited by 1 — ... icon-html.png Access to full text. icon representing file type: icon-pdf.png Full (​PDF) ... In Differential geometry, Peñíscola 1985, volume 1209 of Lecture Notes in Math., pages 66–72. Springer, Berlin ... J. Geom. Anal., 13(2) :233–267, 2003. ... Zbl0423.53032MR535700; Richard Schoen and Shing Tung Yau. On the proof​ .... Results 1 - 15 of 15 — SY94 R. Schoen and S.-T. Yau, Lectures on differential geometry.17 Feb ... (PDF) Differential Geometry of Special Mappings - ResearchGate. ... 1571461981 ISBN​-13: 978-1-57146-198-8 / 9781571461988: Need it Fast?. by J Mikeš · 2021 — One of key analytical methods for differential geometry is the celebrated Bochner ... Schoen, R.; Yau, S.-T. Lectures on Differential Geometry; Int. Press: ... 13. Stepanov, S.E.; Tsyganok, I.I. Theorems of existence and of .... May 19, 2021 — Jeffrey lee, manifolds and differential geometry, chapters 12 and 13 ... The pdf file of the lectures can be found on duo (under other resources). ... Lectures on differential geometry: richard schoen, shing-tung yau: amazon.. by M Berger · 1997 · Cited by 5 — most of the topics of differential geometry, even Riemannian bundles. This is a ... Polytechnicum who all invited me to give lectures, Roma in 1992,. Bombay in .... Shing-Tung Yau is an American mathematician and the William Caspar Graustein Professor of ... In differential geometry, Yau's theorem is significant in proving the general ... Schoen and Yau identified a simple but novel way of inserting the ... Schoen, R.; Yau, S.-T. Lectures on differential geometry. Lecture ... 13, 613–663.. The Ricci flow of a geometry with maximal isotropy SO (3). 11. 6. ... Gromov-​Lawson and Schoen-Yau classified 3-manifolds with positive scalar curvature .... by M Gromov · 2019 — 13. 1Besides these, something is achieved with the Hamilton's Ricci flow, especially in ... Schoen and Yau in [SY(structure) 1979] was a suitably rewritten Gauss formula, ... differential geometry, but, I guess, it may be found in some algebraic articles ... //users.ictp.it/~pub_off/lectures/lns009/Stolz/Stolz.pdf.. Aug 18, 2020 — Schoen Yau Lectures On Differential Geometry 13.pdf lectures on differential geometry schoen, richard schoen and shing-tung yau lectures on .... May 13, 2021 — [ pdf ] the following are some other textbooks that contain basic ... Lectures on differential geometry: richard schoen, shing-tung yau: amazon. ... Last updated on dec 13, 2019 a beginner's course on differential geometry.. Lectures onDifferential Geometry SERIES ON UNIVERSITY MATHEMATICS Editors: W Y Hsiang: Department of Mathematics,.... by Z SHEN · Cited by 18 — Geometry, Milnor Conjecture, Dyadic Solenoid. ... In Section 5 we present Schoen-Yau's proof that three ... [13] S. Y. Cheng and S. T. Yau, Differential equa- ... 3, 333–341. [39] R. Schoen and. S-T. Yau,. Lectures on differential geometry.. In Geometry seminar “Luigi Bianchi” (Pisa, 1982), volume 1022 of Lecture Notes in Math., ... Math., 13:185–208, 1835. 312. ... NASA Technical Note, TN D-5541, 1970. https://ntrs.nasa.gov/archive/nasa/ casi.ntrs.nasa.gov/19700020472.pdf. ... J. Differential Geom., 18(4):791–809 (1984), 1983. 314. R. Schoen and S. T. Yau.. Schoen and S. T. Yau, Proof of the Positive Mass Theorem, II, Comm. Math. Phys. 79 (1981). 231-260. [ .... by Y Lin · 2010 · Cited by 178 — Yau is proved to be a graph with Ricci curvature bounded below by zero. ... [11] R​. Schoen and S. T. Yau, Lecture on Differential Geometry, International Press .... by S Kim · Cited by 23 — of Yau for positive harmonic functions on Riemannian man- ... [13] R. Schoen and S.-T. Yau, Lectures on Differential Geometry, International .... Jan 23, 2021 — Schoen Yau Lectures On Differential Geometry Pdf 13 |WORK|. schoen yau lectures on differential geometry, richard schoen and shing-tung yau .... The Choi-Schoen theorem (PDF). ... The goal of this talk is to prove the following Theorem of Choi & Schoen [1]. Theorem 1. Let N be a ... compact Riemannian manifold with positive Ricci curvature satisfies the estimates (13) and (14). ... The first Theorem is due to Yang & Yau [8]. ... Yau. Lectures on differential geometry.. by O Munteanu · 2021 — from the work of Schoen and Yau [18, 19, 20] on stable minimal surfaces in three- dimensional manifolds. Ric (∇G, ∇G) |∇G|. −2 = 1. 2S −. 1.. ... Calabi-Yau problem in minimal surface theory, see [13], [21], [229], [230] and [​166] for the ... differential geometry, are likely to find some of these problems accessible to ... (Schoen, Yau) and the Penrose Conjecture (Bray) in mathematical physics, ... (Berlin, 1990), volume 1481 of Lecture Notes in Mathematics, pages.. by SYA Chang · Cited by 23 — in conformal geometry of three and four dimensions. We discuss an ... R.Schoen and S.T. Yau; Lectures on Differential Geometry, International Press,. 1994. [V].. by L Ji · 2010 — 13. Solution to the positive mass conjecture in general relativity (1979-1981) ... [​94-8] R. Schoen, S.T. Yau, Lectures on differential geometry, .... by O Chodosh · 2019 · Cited by 10 — The strategy of M. Anderson and L. Rodríguez [2] was refined by G. Liu [13] to ... The following result is due to R. Schoen and S.-T. Yau [22, sec. 5], except for ... dard results in geometric measure theory, we may pass these surfaces to a subse​- ... J. Differential Geometry 6 (1971/72), 119–128. ... Advanced Lectures in.. Available at http://www.numdam.org/article/MSM_1927__25__1_0.pdf. Droste, J. ... On the method of theoretical physics (The Herbert Spencer lecture, delivered at Oxford, ... University Press). https://einsteinpapers.press.princeton.edu/vol13-doc/​. ... The Foundations of Differential Geometry (Cambridge University Press).. by J Lafferty · 2004 · Cited by 288 — sion for the heat kernel that is of great use in differential geometry. This results in a kernel ... for spectral methods in Riemannian geometry is Schoen and Yau (​1994). Readers ... (13) which is easily solved to obtain aj(t) = e−j2t and therefore f(θ, t) = ∑∞ ... Yau. Lectures on Differential Geometry, volume 1 of.. D. Several surveys of mesh parameterization methods can be found in [13,15,3,4]​. Parameterizations ... However, it is well known in differential geometry that distance preserving ... R. Schoen and S.T. Yau, Lectures on Differential Geometry​.. Richard Schoen (Stanford University). Shing-Tung Yau (Harvard University). Original Publication: ... It describes the major achievements in Differential Geometry, which progressed rapidly in the 20th century. Preview (PDF). Publications. Pub. Date. ISBN-13. ISBN-10. Medium. Binding. Size, Etc. Status. List Price. 2010 May.. by DX Kong — and parabolic partial differential equations to differential geometry and physics (​see [26]). There ... Schoen-Yau's solution of the positive mass conjecture (see [24​]-[25]). ... happens if the initial curve is not a graph, e.g., a closed curve? 13 ... [11] D.-X. Kong, Lectures on Quasilinear Hyperbolic Systems and .... Schoen yau lectures on differential geometry pdf 13 download 85ea advanced lectures in mathematics volume xvii geometry and analysis no. Lectures on .... by RM Schoen · 2017 — Richard M. Schoen ... 13. 1. Manifolds admitting metrics with positive scalar curvature. 13. 2. ... the study of differential geometry, there are three types of curvatures that has received a ... proved that the Calabi-Yau metric g0 is a local maximum.. This volume documents the full day course Discrete Differential Geometry: An ... A chapter-by-chapter synopsis The course notes are organized similarly to the lectures. ... ACM Transactions on Graphics 13, 2, 103–136. ... TAO User Manual (​Revision 1.7). ... using progressive mesh [Gu and Yau 2003]), with a worst case.. This book, lectures on differential geometry, by schoen and yau, has two breath-​taking chapters which are big lists of open problems in differential geometry.. May 12, 2021 — (8474 views) lectures on differential geometry by wulf rossmann ... This volume presents lectures given by richard schoen and shing-tung yau at the institute for ... [ pdf ] the following are some other textbooks that contain basic ... Last updated on dec 13, 2019 a beginner's course on differential geometry.. ago introduced me to differential geometry in his eccentric but thoroughly enlightening ... aged me to turn my lecture notes into a book and gave me free rein in de- ... Tensors on a Vector Space. 13. If (E1,...,En) is a basis for V , we let (​ϕ. 1. ,...,ϕ n. ) ... Richard Schoen; see [LP87] for an expository account of Schoen's solution.. by S KIM · Cited by 23 — consequence, we give another proof to Harnack inequality of Yau for positive ... [​13] R. Schoen and S.-T. Yau, Lectures on differential geometry, International .... Global differential geometry, 170–222, MAA Stud. Math. ... 13 (1980), 451–469. ... Lecture Notes Series 6, Seoul National University, 1993. http://math.uci.edu/ pli/lecture.pdf. ... [119] Li, Peter; Schoen, Richard. ... Math. J. 48 (1999), 1257–1284. Li, Peter; Yau, Shing-Tung. On the parabolic kernel of the Schrödinger operator.. by T Eguchi · 1980 · Cited by 2193 — Gravitation, gauge theories and differential geometry ... Article Download PDF​View Record in ScopusGoogle Scholar ... Lecture at the 12th Winter School at the Leningrad Nuclear Physics Institute, SLAC Translation, 176 ... Schoen and Yau, 1978 ... 13th Biennial Seminar, Canadian Mathematical Congress (1972), pp. 1-​40.. Jul 9, 2012 — Advanced Lectures in Mathematics 20, International Press, Boston, 2011, ISBN 978-1-57146- ... [SY94] R. Schoen and S.-T. Yau, Lectures on differential geometry, Conference Proceedings and ... CAG-13-5-845-885.pdf.. [13] Yau, Shing-Tung, Non-existence of continuous convex functions on certain ... [164] *Lectures on Differential Geometry, Yau, Shing-Tung and R. Schoen, .... by C Sormani · 2000 · Cited by 17 — Tung Yau proved that a complete noncompact manifold with nonnegative ... (13). Since b−1(r) is compact, there exists xr,yr ∈ b−1(bmin + r) such that ... [SchYau] R. Schoen and S.-T. Yau, Lectures on Differential Geometry, Conference Pro-.. Seminar on Differential Geometry. ... The basic tools will be partial differential equations while the basic motivation is to settle ... The following is a lecture on the Blaschke conjecture given at the Institute for ... Richard Schoen and Yau Shing-Tung ... As many authors have pointed out (for example see [2] and [13]), the Ricci .... 118 results — PDF icon Onsager96.pdf (523.23 KB) ... Journal of Differential Geometry. 69:75–​110. ... 2006/2007:175–203. PDF icon Exp.972.C.DeLellis.pdf (248.93 KB). Crippa G. ... 55:1–13. PDF icon Gian_Ind.pdf (221.59 KB). Ambrosio L., De Lellis C., Schmidt T.. 2018. ... Zurich Lectures in Advanced Mathematics. 7 PDF .... [13] William Meeks III, Shing-Tung Yau; Topology of three- dimensional ... Lecture Notes, p.13-47, 2017. Meeting on ... http://www.math.sunysb.edu/ anderson/​compactif.pdf ... [33] R. Schoen, & S. T. Yau, Lectures on Differential Geometry.. Schoen/Yau, "Lectures on Differential Geometry" (1994). This is about as advanced as it gets. You need to read at least 5 other DG books before starting this one .... geometry, including, differential equations on a manifold and the relation between ... Reference : R. Schoen and S.-T. Yau, Lectures on Differential Geometry, ... Time: 13:30 - 14:45, Tuesday,Thursday, September 10, 2013 - January 10, 2014.. Buy Lectures on Differential Geometry (2010 re-issue) on Amazon.com ✓ FREE ... ISBN-10 ‏ : ‎ 1571461981; ISBN-13 ‏ : ‎ 978-1571461988; Item Weight ‏ : ‎ 2.01 ... This book, Lectures on Differential Geometry , by Schoen and Yau, has two .... by R Schoen · Cited by 1424 — Chapter 9: Open Problems in Differential Geometry ... 13 Harmonic Maps and the Topology of Stable Hypersurfaces ... Authors: R. Schoen and S. T. Yau.. Contents. 1 Week 1: Introduction to General Relativity; Differential Geometry I (​Apr. 07) ... 5–13), Concepts of Mass in Classical and Modern Physics. 7. ... Schoen and Yau (1983), “The Existence of a Black Hole Due to Condensation of Matter”. 18. ... Conference version available at http://www1.mate.polimi.it/bh2/​Ansoldi.pdf.. Thesis, University of Utah, http://www.math.utah.edu/theses/2002/thornton/blake-​thorntondissertation.pdf, 2002.. was the tenth in a family of thirteen children .... Feb 28, 2018 — Schoen/Yau, "Lectures on Differential Geometry" . edited Apr 13 '17 at 12:58.. Minimal Submanifolds in Di erential Geometry Richard Schoen .... by TH COLDING · Cited by 38 — The conjectures were again revisited in Yau's 2000 millenium lecture (see page ... and differential geometry in the large, Comment. Math. Helv. 32. 1957 13–72. ... [Sc1] R. Schoen, Estimates for stable minimal surfaces in three-dimensional .... May 6, 2021 — Lectures on differential geometry (pdf 221p) this note contains on the following ... Jeffrey lee, manifolds and differential geometry, chapters 12 and 13 - center ... Buy lectures on differential geometry by schoen, richard, yau, .... by PWK Li · 2014 · Cited by 5 — Differential Geometry and Partial Differential Equations ... Co-Editor (with Lizheng Ji, Richard Schoen, and Leon Simon), “Handbook of Geometric Analysis, Vol. ... Yau with Commentary” Advanced Lectures in Mathematics, 28, Vol I & II, ... with B​. Chow, Z. Lu, and L. Ni, 13th Southern California Geometric Analysis Seminar,.. by J LOFTIN · Cited by 6 — GEOMETRY AND THE “Y” VERTEX. JOHN LOFTIN ... Main Result. There exist many nontrivial semi-flat Calabi-Yau struc- ... Let U be a nonzero holomorphic cubic differential on CP1 with exactly 3 poles ... We proceed as in e.g. Schoen-​Yau ... Global Differential Geometry and Global Analysis, volume 1481 of Lecture Notes.. by BO Kim · 1998 — 13 (1998), No. ... In 2], Li-Yau used Fourier transform to estimate the lower bound of ... [5] R. Schoen, S. T. Yau, Lectures on Differential Geometry, International .... by V Bonini · 2016 · Cited by 2 — In [16], using hyperbolic Gauss maps and the geometry of horospheres, Epstein showed that ... We will rely on the injectivity theorem of Schoen and Yau [25, 26], while Epstein [16] ... Karcher [13] and a Harnack-type estimate from Li and Schoen [22]. ... [26] R. Schoen, S.T. Yau, Lectures on Differential Geometry (​Conference .... by W Zeng · Cited by 37 — fer readers to the differential geometry textbook [23]. For more ... work [22], discrete Ricci flow work [12, 13] and Yamabe flow ... [23] R. M. Schoen and S.-T. Yau. ... [28] W. P. Thurston. Geometry and topology of three-manifolds. Lecture.. Writing a readable introduction to differential geometry is among the most difficult feats in the art of mathematical exposition. Such an introduction should ideally .... by W Rossmann · Cited by 4 — on manifolds, tensor analysis, and differential geometry. I offer them to ... 13. Let M be a manifold, p ∈ M a point of M. Let Mp be the set of all points which can be​ .... settled by Schoen and Yau [163,164] in space-dimension lower than or ... (1.1.13​) where δ denotes the flat Euclidean metric in the coordinate system (yi). ... while the differential-geometric definitions of Ji do not involve a square root of minus .... PDF PDF Hitchins Lecture Notes on Differentiable Manifolds here A ... Publisher World Scientific Publishing Company 2009 ISBNASIN 9812708537 ISBN-13 9789812708533 Number ... Lectures on Differential Geometry Schoen R., Yau S.​-T.. Course homepage: http://math.arizona.edu/>glickenstein/math537. Textbook: ... Lectures on Differential Geometry, by R. Schoen and S. T. Yau. Comparison ... 12​#13. Spectral geometry. 14. Einstein manifolds, curvature functionals, Ricci flow.. by S Brendle · 2006 · Cited by 2 — The partial differential equation (2) is closely related to the Ricci flow in dimen- sion 2. ... (see [13]), and is based on pinching estimates for the eigenvalues of the Ricci tensor. ... [35] Schoen, R. M., Yau, S. T., Lectures on differential geometry.. Aug 27, 2018 — This course as taught by Shing-Tung Yau. The lectures were given in the. CMSA building room G10, at TTh 1-2:30. There were no official .... S.T. Yau, R. Schoen, On the structure of manifolds with positive scalar curvature. ... arXiv:1612.07505 13. ... J. Rosenberg, Manifolds of positive scalar curvature: a progress report. in Surveys on Differential Geometry, vol. ... Problems. www.ihes.fr/gromov/PDF/Morse-Spectra-April16-2015-.pdf 23. ... Lecture Notes, 15, Amer.. Math. Soc. 5 (1954), 801–807. , Medians, lattices and trees, Proc. Amer. Math. ... 13 (2001), no. ... R. Schoen and S.-T. Yau, Lectures on differential geometry, Conference Proceedings and Lecture Notes ... Ph.D. Thesis, University of Utah, http://www.math.utah.edu/theses/2002/thornton/blake-thorntondissertation.pdf, 2002.

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