Locally convex aspects of the Kato and the Dynkin classes on manifolds

DOI10.1215/00192082-11621880MaRDI QIDQ6670902

Kazuhiro Kuwae, Batu Güneysu

Publication date: 24 January 2025

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Ricci curvatureheat kernelKato classRiemann manifoldDynkin class

Mathematics Subject Classification ID

Dirichlet forms (31C25) Heat equation (35K05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Schrödinger and Feynman-Kac semigroups (47D08) Heat kernel (35K08)

Cites Work

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• Heat kernel bounds on metric measure spaces and some applications
• Path integrals and the essential self-adjointness of differential operators on noncompact manifolds
• Heat kernels in the context of Kato potentials on arbitrary manifolds
• Functions with bounded variation on a class of Riemannian manifolds with Ricci curvature unbounded from below
• Kato class measures of symmetric Markov processes under heat kernel estimates
• Diffusion processes and heat kernels on metric spaces
• Covariant Schrödinger semigroups on Riemannian manifolds
• Perturbation of Dirichlet forms by measures
• Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature
• Geometric inequalities for manifolds with Ricci curvature in the Kato class
• Schrödinger operators with singular potentials
• Geometric and spectral estimates based on spectral Ricci curvature assumptions
• Kac regular sets and Sobolev spaces in geometry, probability and quantum physics
• The Kato class on compact manifolds with integral bounds on the negative part of Ricci curvature
• Schrödinger semigroups
• Brownian motion and harnack inequality for Schrödinger operators
• CONTINUITY PROPERTIES OF SCHRÖDINGER SEMIGROUPS WITH MAGNETIC FIELDS
• Kato’s inequality and form boundedness of Kato potentials on arbitrary Riemannian manifolds
• Torus stability under Kato bounds on the Ricci curvature

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