Dimension-free Harnack inequalities for conjugate heat equations and their applications to geometric flows
DOI10.2140/apde.2023.16.1589zbMath1530.35118arXiv2010.04916OpenAlexW3091875108MaRDI QIDQ6185899
Li-Juan Cheng, Anton Thalmaier
Publication date: 9 January 2024
Published in: Analysis \& PDE (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2010.04916
heat equationHarnack inequalityFeynman-Kac formulalog-Sobolev inequalityBismut formulageometric flow
Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Fundamental solutions to PDEs (35A08) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Heat kernel (35K08)
Cites Work
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- Sobolev-type inequalities and heat kernel bounds along the geometric flow
- Harnack estimates for conjugate heat kernel on evolving manifolds
- Gaussian upper bounds for the heat kernel on arbitrary Riemannian manifolds
- The Harnack estimate for the Ricci flow
- Harnack inequality for SDE with multiplicative noise and extension to Neumann semigroup on nonconvex manifolds
- Log-Sobolev inequality on non-convex Riemannian manifolds
- Large deviations and the Malliavin calculus
- A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
- Formulae for the derivatives of heat semigroups
- Derivatives of Feynman-Kac semigroups
- Evolution systems of measures and semigroup properties on evolving manifolds
- Diffusion semigroup on manifolds with time-dependent metrics
- Analysis for Diffusion Processes on Riemannian Manifolds
- Bounds on the heat kernel under the Ricci flow
- Differential Harnack estimates for conjugate heat equation under the Ricci flow
- Explicit Constants for Gaussian Upper Bounds on Heat Kernels
- Logarithmic Sobolev Inequalities
- On the differentiation of heat semigroups and poisson integrals
- Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
- Heat Kernel Coupled with Geometric Flow and Ricci Flow
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