Geometric Analysis by Peter Li (English) Hardcover Book

Description: Geometric Analysis by Peter Li This graduate-level text demonstrates the basic techniques and how to apply them to various areas of research in geometric analysis. The author focuses mainly on the interaction of partial differential equations with differential geometry and only a rudimentary knowledge of Riemannian geometry and partial differential equations is required. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description 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 authors own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field. Author Biography Peter Li is Chancellors Professor at the University of California, Irvine. Table of Contents Introduction; 1. First and second variational formulas for area; 2. Volume comparison theorem; 3. Bochner–Weitzenböck formulas; 4. Laplacian comparison theorem; 5. Poincaré inequality and the first eigenvalue; 6. Gradient estimate and Harnack inequality; 7. Mean value inequality; 8. Reillys 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, Poincaré inequality and parabolic mean value inequality; 15. Uniqueness and maximum principle for the heat equation; 16. Large time behavior of the heat kernel; 17. Greens function; 18. Measured Neumann–Poincaré 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. Review "This monograph is a beautiful introduction to geometric analysis."Frederic Robert, Mathematical Reviews Promotional This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis. Review Quote "This monograph is a beautiful introduction to geometric analysis." Frederic Robert, Mathematical Reviews Promotional "Headline" This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis. Description for Bookstore This graduate-level text demonstrates the basic techniques and how to apply them to various areas of research in geometric analysis. The author focuses mainly on the interaction of partial differential equations with differential geometry and only a rudimentary knowledge of Riemannian geometry and partial differential equations is required. Description for Library This graduate-level text demonstrates the basic techniques and how to apply them to various areas of research in geometric analysis. The author focuses mainly on the interaction of partial differential equations with differential geometry and only a rudimentary knowledge of Riemannian geometry and partial differential equations is required. Details ISBN1107020646 Author Peter Li Year 2012 ISBN-10 1107020646 ISBN-13 9781107020641 Media Book Publisher Cambridge University Press Series Cambridge Studies in Advanced Mathematics Imprint Cambridge University Press Place of Publication Cambridge Country of Publication United Kingdom DEWEY 515.1 Short Title GEOMETRIC ANALYSIS Language English Series Number 134 Publication Date 2012-05-03 Pages 418 Illustrations black & white illustrations Affiliation University of California, Irvine Format Hardcover UK Release Date 2012-05-03 AU Release Date 2012-05-03 NZ Release Date 2012-05-03 Alternative 9781139105798 Audience Postgraduate, Research & Scholarly We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:160314945;

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