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<図書>
Geometric analysis

責任表示 Peter Li
シリーズ Cambridge studies in advanced mathematics ; 134
データ種別 図書
出版者 Cambridge : Cambridge University Press
出版年 2012
本文言語 英語
大きさ x, 406 p. ; 24 cm
概要 "The aim of this graduate-level text is to equip the reader with the basic tools and techniques needed for research in various areas of geometric analysis. Throughout, the main theme is to present the...interaction of partial differential equations and differential geometry. More specifically, emphasis is placed on how the behavior of the solutions of a PDE is affected by the geometry of the underlying manifold and vice versa. For efficiency the author mainly restricts himself to the linear theory and only a rudimentary background in Riemannian geometry and partial differential equations is assumed. Originating from the author's own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field"--続きを見る
目次 Machine generated contents note: Introduction; 1. First and second variational formulas for area; 2. Volume comparison theorem; 3. Bochner-Weitzenböck formulas; 4. Laplacian comparison theorem; 5. Poincare; inequality and the first eigenvalue; 6. Gradient estimate and Harnack inequality; 7. Mean value inequality; 8. Reilly's formula and applications; 9. Isoperimetric inequalities and Sobolev inequalities; 10. The heat equation; 11. Properties and estimates of the heat kernel; 12. Gradient estimate and Harnack inequality for the heat equation; 13. Upper and lower bounds for the heat kernel; 14. Sobolev inequality, Poincare; inequality and parabolic mean value inequality; 15. Uniqueness and maximum principle for the heat equation; 16. Large time behavior of the heat kernel; 17. Green's function; 18. Measured Neumann-Poincare; inequality and measured Sobolev inequality; 19. Parabolic Harnack inequality and regularity theory; 20. Parabolicity; 21. Harmonic functions and ends; 22. Manifolds with positive spectrum; 23. Manifolds with Ricci curvature bounded from below; 24. Manifolds with finite volume; 25. Stability of minimal hypersurfaces in a 3-manifold; 26. Stability of minimal hypersurfaces in a higher dimensional manifold; 27. Linear growth harmonic functions; 28. Polynomial growth harmonic functions; 29. Lq harmonic functions; 30. Mean value constant, Liouville property, and minimal submanifolds; 31. Massive sets; 32. The structure of harmonic maps into a Cartan-Hadamard manifold; Appendix A. Computation of warped product metrics; Appendix B. Polynomial growth harmonic functions on Euclidean space; References; Index.
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所蔵情報


理系図3F 数理独自 033212012001592 LI,/27/1 2012

書誌詳細

著者標目 *Li, P. (Peter)
件 名 LCSH:Geometric analysis
FREE:MATHEMATICS / Geometry / General. bisacsh
分 類 LCC:QA360
DC23:515/.1
書誌ID 1001477487
ISBN 9781107020641
NCID BB09064047
巻冊次 ISBN:9781107020641
登録日 2012.05.23
更新日 2017.03.14

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