Grigor'yan Alexander, Sun Yuhua (Eds.) Analysis and Partial Differential Equations on Manifolds, Fractals and Graphs

De Gruyter, 2021. — 526 p. — (Advances in Analysis and Geometry). — ISBN 10 3110700638, 13 978-3110700633.The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.PrefaceFractals and graphsStability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes
The pointwise existence and properties of heat kernel
Resistance estimates and critical exponents of Dirichlet forms on fractals
A survey on unbounded Laplacians and intrinsic metrics on graphs
Energy measures for diffusions on fractals: a survey
Hyperbolic graphs induced by iterations and applications in fractals
Geometric implications of fast volume growth and capacity estimates
Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set
Metrics and uniform Harnack inequality on the Strichartz hexacarpetEuclidean spaces and manifoldsAnalysis on manifolds and volume growth
Geometric analysis on manifolds with ends
A matrix Harnack estimate for a Kolmogorov type equation
Entropy power concavity inequality on Riemannian manifolds and Ricci flow
Fractional differential operators and divergence equations
Interior gradient estimates for mean curvature type equations and related flows
An alternate induction argument in Simons’ proof of holonomy theorem
Higher integrability for nonlinear nonlocal equations with irregular kernel
On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds
Index