紀錄類型: |
書目-電子資源
: Monograph/item
|
正題名/作者: |
Geometric analysis/ by Peter Li. |
作者: |
Li, Peter, |
出版者: |
Cambridge :Cambridge University Press, : 2012., |
面頁冊數: |
x, 406 p. :digital ;24 cm. |
內容註: |
Machine generated contents note: Introduction; 1. First and second variational formulas for area; 2. Volume comparison theorem; 3. Bochner-Weitzenbock 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. |
標題: |
Geometric analysis. - |
電子資源: |
https://doi.org/10.1017/CBO9781139105798 |
ISBN: |
9781139105798 |