Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs

DOI10.1515/crelle-2017-0038zbMath1432.35213arXiv1411.5087OpenAlexW2766139843MaRDI QIDQ2009893

Shuang Liu, Yong Lin, Paul S. Horn, Shing Tung Yau

Publication date: 2 December 2019

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5087

zbMATH Keywords

logarithmic Sobolev inequalityPoincaré inequalityheat semigroupvolume doublingcurved graphsGaussian heat kernel estimate

Mathematics Subject Classification ID

Heat equation (35K05) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Signed and weighted graphs (05C22) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Heat kernel (35K08) PDEs on manifolds (35R01) PDEs on graphs and networks (ramified or polygonal spaces) (35R02)

Related Items (23)

The existence and nonexistence of global solutions for a semilinear heat equation on graphs ⋮ Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature ⋮ Ricci curvature of Bruhat orders ⋮ Curvature on graphs via equilibrium measures ⋮ Blow-up on metric graphs and Riemannian manifolds ⋮ Normalized solutions for nonlinear Schrödinger equations on graphs ⋮ \(\psi\)-Li-Yau inequality for the \(p\)-Laplacian on weighted graphs with the \(CD_p^\psi (m, 0)\) curvature ⋮ Rigidity properties of the hypercube via Bakry-Émery curvature ⋮ Blow-up conditions for a semilinear parabolic system on locally finite graphs ⋮ Topological degree for Chern-Simons Higgs models on finite graphs ⋮ Unnamed Item ⋮ Curvature and Higher Order Buser Inequalities for the Graph Connection Laplacian ⋮ Perpetual cutoff method and \(CDE^{\prime} (K, N)\) condition on graphs ⋮ Discrete versions of the Li-Yau gradient estimate ⋮ Unnamed Item ⋮ Inner-outer curvatures, Ollivier-Ricci curvature and volume growth of graphs ⋮ Bakry–Émery Curvature Functions on Graphs ⋮ Ultracontractive Properties for Directed Graph Semigroups with Applications to Coupled Oscillators ⋮ Distance bounds for graphs with some negative Bakry-Émery curvature ⋮ The entropy method under curvature-dimension conditions in the spirit of Bakry-Émery in the discrete setting of Markov chains ⋮ Li-Yau Gradient Estimate on Graphs ⋮ Heat kernel and monotonicity inequalities on the graph ⋮ Bakry-Émery curvature on graphs as an eigenvalue problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Heat kernel bounds on metric measure spaces and some applications
• Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
• Diffusion determines the recurrent graph
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries
• Perelman's entropy and doubling property on Riemannian manifolds
• Generalized Liouville properties of manifolds
• Logarithmic Harnack inequalities
• Gaussian estimates for Markov chains and random walks on groups
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• Analysis of the physical Laplacian and the heat flow on a locally finite graph
• On the parabolic kernel of the Schrödinger operator
• Nonlinear analysis in geometry
• Random walks on graphs with regular volume growth
• Harnack inequalities on a manifold with positive or negative Ricci curvature
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Harmonic sections of polynomial growth
• Markov chain approximations to symmetric diffusions
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• Parabolic Harnack inequality for divergence form second order differential operators
• Remarks on logarithmic Sobolev constants, exponential integrability and bounds on the diameter
• Laplacians on infinite graphs: Dirichlet and Neumann boundary conditions
• Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory
• Ricci curvature and eigenvalue estimate on locally finite graphs
• Li-Yau inequality on graphs
• Holomorphic completions, analytic continuation, and the interpolation of semi-norms
• On the geometry of metric measure spaces. II
• Lectures on summability
• Dirichlet forms and stochastic completeness of graphs and subgraphs
• A note on the isoperimetric constant
• Heat Kernels of Graphs
• Large Deviations for Heat Kernels on Graphs
• Eigenvalue Ratios of Non-Negatively Curved Graphs
• Heat kernel and essential spectrum of infinite graphs

This page was built for publication: Volume doubling, Poincaré inequality and Gaussian heat kernel estimate for non-negatively curved graphs