Geometry and analysis of Dirichlet forms. II

DOI10.1016/j.jfa.2014.07.015zbMath1297.53033OpenAlexW1979741489WikidataQ109994421 ScholiaQ109994421MaRDI QIDQ403329

Pekka Koskela, Nageswari Shanmugalingam, Yuan Zhou

Publication date: 29 August 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2014.07.015

zbMATH Keywords

Dirichlet formBakry-Emery's Ricci curvatureBoltzman-Shannon entropyCheeger energy functionallocal Poincaré inequalitiesriemannian Ricci curvature

Mathematics Subject Classification ID

Heat equation (35K05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items

Optimal transport, Cheeger energies and contractivity of dynamic transport distances in extended spaces ⋮ Diffusion, optimal transport and Ricci curvature ⋮ Hölder classes via semigroups and Riesz transforms ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ The bounded variation capacity and Sobolev-type inequalities on Dirichlet spaces ⋮ The intrinsic Hopf-Lax semigroup vs. the intrinsic slope ⋮ Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds ⋮ On Dirichlet forms and semi-Dirichlet forms. Remarks on the book ``Semi-Dirichlet forms and Markov processes by Yoichi Oshima ⋮ Neumann problem for \(p\)-Laplace equation in metric spaces using a variational approach: existence, boundedness, and boundary regularity ⋮ Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
• \(L^\infty\)-variational problem associated to Dirichlet forms
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• Functional inequalities and Hamilton-Jacobi equations in geodesic spaces
• Geometry and analysis of Dirichlet forms
• Intrinsic geometry and analysis of diffusion processes and \(L^{\infty}\)-variational problems
• Duality on gradient estimates and Wasserstein controls
• Semigroups of linear operators and applications to partial differential equations
• Quasiconformal maps in metric spaces with controlled geometry
• Differentiability of Lipschitz functions on metric measure spaces
• Dirichlet forms and symmetric Markov processes
• Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type
• On the structure of spaces with Ricci curvature bounded below. I
• Heat kernel asymptotics and the distance function in Lipschitz Riemannian manifolds
• Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces
• Hypoelliptic heat kernel inequalities on the Heisenberg group
• A differentiable structure for metric measure spaces
• Newtonian spaces: An extension of Sobolev spaces to metric measure spaces
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Is a diffusion process determined by its intrinsic metric?
• Ricci curvature for metric-measure spaces via optimal transport
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Transport inequalities, gradient estimates, entropy and Ricci curvature
• DIRICHLET SPACES
• A dual characterization of length spaces with application to Dirichlet metric spaces
• Gradient flows on Wasserstein spaces over compact Alexandrov spaces
• Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
• Real Analysis and Probability
• Heat Flow on Alexandrov Spaces
• Optimal Transport
• On the relation between elliptic and parabolic Harnack inequalities