Heat kernel bounds on metric measure spaces and some applications

DOI10.1007/s11118-015-9521-2zbMath1339.53043arXiv1407.5289OpenAlexW2963940944MaRDI QIDQ283385

Hui-Chun Zhang, Huai-Qian Li, Ren Jin Jiang

Publication date: 13 May 2016

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.5289

zbMATH Keywords

heat equationRicci curvatureheat kernelRiesz transformmetric measure space

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Heat equation (35K05) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Heat kernel (35K08)

Related Items (41)

Littlewood-Paley-Stein functions for non-local Schrödinger operators ⋮ Some weighted norm inequalities on manifolds ⋮ Boundary regularity and stability for spaces with Ricci bounded below ⋮ Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature ⋮ Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel ⋮ Spectral multipliers on exponentially locally doubling metric measure spaces ⋮ Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions ⋮ Exponential integrability and exit times of diffusions on sub-Riemannian and metric measure spaces ⋮ Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds ⋮ Radial processes on \(\mathsf{RCD}^\ast(K,N)\) spaces ⋮ Singular Weyl’s law with Ricci curvature bounded below ⋮ A note on the topological stability theorem from RCD spaces to Riemannian manifolds ⋮ Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability ⋮ Calculus and fine properties of functions of bounded variation on RCD spaces ⋮ \(L^p\)-independence of spectral radius for generalized Feynman-Kac semigroups ⋮ Short-time behavior of the heat kernel and Weyl's law on \(\mathrm{RCD}^*(K,N)\) spaces ⋮ Monotonicity formulas for harmonic functions in \(\mathrm{RCD}(0,N)\) spaces ⋮ Essential spectrum and Feller type properties ⋮ Sobolev mappings between RCD spaces and applications to harmonic maps: a heat kernel approach ⋮ Regularity of Lagrangian flows over \(\operatorname{RCD}^*(K, N)\) spaces ⋮ Wasserstein convergence rates for empirical measures of subordinated processes on noncompact manifolds ⋮ Removable sets and \(L^p\)-uniqueness on manifolds and metric measure spaces ⋮ Isometric immersions of \(\mathrm{RCD}(K, N)\) spaces via heat kernels ⋮ New differential operator and noncollapsed RCD spaces ⋮ Monotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spaces ⋮ A PDE approach to a 2-dimensional matching problem ⋮ Sharp heat kernel bounds and entropy in metric measure spaces ⋮ Dimension-free Harnack inequalities on \(\mathrm{RCD}(K, \infty )\) spaces ⋮ Improved regularity estimates for Lagrangian flows on \(\mathrm{RCD}(K,N)\) spaces ⋮ Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and \(\mathrm{RCD}(K,\infty)\) spaces ⋮ Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs ⋮ Restriction of heat equation with Newton-Sobolev data on metric measure space ⋮ Convergence to the product of the standard spheres and eigenvalues of the Laplacian ⋮ Convergence of Brownian motions on metric measure spaces under Riemannian curvature-dimension conditions ⋮ Second order differentiation formula on \(\mathsf{RCD}^*(K,N)\) spaces ⋮ Localized elliptic gradient estimate for solutions of the heat equation on \({ RCD}^\ast(K,N)\) metric measure spaces ⋮ Isometric immersions of RCD spaces ⋮ Rigidity of the 1-Bakry-Émery inequality and sets of finite Perimeter in RCD spaces ⋮ Weighted Littlewood-Paley inequalities for heat flows in RCD spaces ⋮ Finer estimates on the \(2\)-dimensional matching problem ⋮ Weakly non-collapsed RCD spaces are strongly non-collapsed

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