Geometric analysis

Geometric analysis

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Auteur principal : Li Peter (Auteur)
Format : Livre
Langue : anglais
Titre complet : Geometric analysis / Peter Li,...
Publié : Cambridge, New York : Cambridge University Press , 2012
Description matérielle : 1 vol. (X-406 p.)
Collection : Cambridge studies in advanced mathematics ; 134
Accès en ligne : Informations complémentaires sur la publication à l'adresse
Sujets :
Analyse globale (mathématiques)
Équations aux dérivées partielles
Géométrie différentielle
Analyse géométrique
Documents associés : Autre format: Geometric analysis
  • 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
  • 1. 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