Contents

Kapitel in diesem Buch

1. Frontmatter I
2. Contents V
3. Preface VII
4. Part I: Fractals and graphs
5. Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes 1
6. The pointwise existence and properties of heat kernel 27
7. Resistance estimates and critical exponents of Dirichlet forms on fractals 71
8. A survey on unbounded Laplacians and intrinsic metrics on graphs 103
9. Energy measures for diffusions on fractals: a survey 119
10. Hyperbolic graphs induced by iterations and applications in fractals 143
11. Geometric implications of fast volume growth and capacity estimates 183
12. Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set 201
13. Metrics and uniform Harnack inequality on the Strichartz hexacarpet 275
14. Part II: Euclidean spaces and manifolds
15. Analysis on manifolds and volume growth 299
16. Geometric analysis on manifolds with ends 325
17. A matrix Harnack estimate for a Kolmogorov type equation 345
18. Entropy power concavity inequality on Riemannian manifolds and Ricci flow 359
19. Fractional differential operators and divergence equations 385
20. Interior gradient estimates for mean curvature type equations and related flows 421
21. An alternate induction argument in Simons’ proof of holonomy theorem 443
22. Higher integrability for nonlinear nonlocal equations with irregular kernel 459
23. On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds 493
24. Index 515