Geometric Analysis (Cambridge Studies in Advanced Mathematics), Peter Li - Shop Online for Books in the United Kingdom

Warehouse Stock Clearance Sale

Grab a bargain today!


Sign Up for Fishpond's Best Deals Delivered to You Every Day
Go
Geometric Analysis
Cambridge Studies in Advanced Mathematics

Rating
Format
Hardback, 418 pages
Published
United Kingdom, 3 May 2012

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.


Our Price
£53.41
Elsewhere
£63.99
Save £10.58 (17%)
Ships from Australia Estimated delivery date: 20th Feb - 28th Feb from Australia
Free Shipping Worldwide

Buy Together
+
Buy together with Cambridge Studies in Advanced Mathematics at a great price!
Buy Together
£94.44
Elsewhere Price
£99.40
You Save £4.96 (5%)

Product 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 author's own lectures, this book is an ideal introduction for graduate students, as well as a useful reference for experts in the field.

Product Details
EAN
9781107020641
ISBN
1107020646
Writer
Other Information
black & white illustrations
Dimensions
22.9 x 15.2 x 2.8 centimeters (0.37 kg)

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. 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, 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. Green's 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.

Promotional Information

This graduate-level text demonstrates the basic techniques for researchers interested in the field of geometric analysis.

About the Author

Peter Li is Chancellor's Professor at the University of California, Irvine.

Reviews

"This monograph is a beautiful introduction to geometric analysis."
Frederic Robert, Mathematical Reviews

Show more
Review this Product
Ask a Question About this Product More...
 
Look for similar items by category
People also searched for
Item ships from and is sold by Fishpond Retail Limited.

Back to top
We use essential and some optional cookies to provide you the best shopping experience. Visit our cookies policy page for more information.