Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel

DOI10.1016/j.jfa.2022.109599zbMath1494.35088arXiv2010.01849OpenAlexW3091622969MaRDI QIDQ2155287

Mathias Braun

Publication date: 15 July 2022

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

Full work available at URL: https://arxiv.org/abs/2010.01849

zbMATH Keywords

Ricci curvaturespectral theoryfunctional inequalitiesheat flowHess-Schrader-Uhlenbrock inequality

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Hodge theory in global analysis (58A14) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Spectral theory; eigenvalue problems on manifolds (58C40) Heat kernel (35K08) PDEs on manifolds (35R01) Ricci flows (53E20)

Related Items (1)

Metric measure spaces and synthetic Ricci bounds: fundamental concepts and recent developments

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Heat kernel bounds on metric measure spaces and some applications
• Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in \(\text{RCD}(K, \infty)\) metric measure spaces
• \(L^p\)-independence of spectral bounds of generalized non-local Feynman-Kac semigroups
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Bakry-Émery curvature-dimension condition and Riemannian Ricci curvature bounds
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
• Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds
• On the \(L^p\) independence of the spectrum of the Hodge Laplacian on non-compact manifolds
• Espaces de Dirichlet. I: Le cas élémentaire
• The Atiyah-Singer theorems: A probabilistic approach. I: The index theorem
• Uniformly elliptic operators on Riemannian manifolds
• On the equivalence of heat kernel estimates and logarithmic Sobolev inequalities for the Hodge Laplacian
• A logarithmic Sobolev form of the Li-Yau parabolic inequality
• \(L^p\)-independence of spectral bounds of Feynman-Kac semigroups by continuous additive functionals
• Analysis of the Laplacian on a complete Riemannian manifold
• \(L^ p\) contractive projections and the heat semigroup for differential forms
• The spectrum of a Schrödinger operator in \(L_ p({\mathbb{R}}^{\nu})\) is p-independent
• On the \(L_ p\)-spectrum of Schrödinger operators
• Kato's inequality and the spectral distribution of Laplacians on compact Riemannian manifolds
• Opérateur de courbure et laplacien des formes différentielles d'une variété riemannienne
• Domination of semigroups and generalization of Kato's inequality
• Kato's inequality and the comparison of semigroups
• \(L^p\) contraction semigroups for vector valued functions
• On the \(L^ p\)-spectrum of uniformly elliptic operators on Riemannian manifolds
• Formulae for the derivatives of heat semigroups
• \(L^ p\) contraction semigroups for vector valued functions
• Ricci tensor on \(\mathrm{RCD}^\ast(K,N)\) spaces
• Covariant Schrödinger semigroups on Riemannian manifolds
• Riesz transform, Gaussian bounds and the method of wave equation
• Perturbation theory for linear operators.
• Introduction to spectral theory. With applications to Schrödinger operators
• Analysis on local Dirichlet spaces. II: Upper Gaussian estimates for the fundamental solutions of parabolic equations
• Analysis on local Dirichlet spaces. III: The parabolic Harnack inequality
• Perturbation of Dirichlet forms by measures
• Gaussian heat kernel estimates: from functions to forms
• Exponential convergence of Markovian semigroups and their spectra on \(L^p\)-spaces
• Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature
• Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds
• \(L^p\)-estimates for the heat semigroup on differential forms, and related problems
• Distribution-valued Ricci bounds for metric measure spaces, singular time changes, and gradient estimates for Neumann heat flows
• Quasi-continuous vector fields on RCD spaces
• Spectral convergence under bounded Ricci curvature
• Ricci curvature for metric-measure spaces via optimal transport
• Structure theory of metric measure spaces with lower Ricci curvature bounds
• The spectrum of continuously perturbed operators and the Laplacian on forms
• Estimates for the heat kernel on differential forms on Riemannian symmetric spaces and applications
• Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
• A Gaussian estimate for the heat kernel on differential forms and application to the Riesz transform
• Metric measure spaces with Riemannian Ricci curvature bounded from below
• \(L^p\)-independence of spectral bounds of Schrödinger type semigroups
• Large time behavior of heat kernels on forms
• An \(L^{2}\) theory for differential forms on path spaces. I
• On the geometry of metric measure spaces. I
• On the geometry of metric measure spaces. II
• Curvature and the eigenforms of the Laplace operator
• Optimal transport, gradient estimates, and pathwise Brownian coupling on spaces with variable Ricci bounds
• Embedding of \(\mathrm{RCD}^\ast (K,N)\) spaces in \(L^2\) via eigenfunctions
• On the differential structure of metric measure spaces and applications
• Lp -independence of spectral bounds of non-local Feynman-Kac semigroups
• Logarithmic Sobolev Inequalities
• Nonsmooth differential geometry– An approach tailored for spaces with Ricci curvature bounded from below
• Analysis and Geometry of Markov Diffusion Operators
• Heat Kernel and Quantum Gravity
• Constancy of the Dimension for RCD(K,N) Spaces via Regularity of Lagrangian Flows
• Riemannian Ricci curvature lower bounds in metric measure spaces with 𝜎-finite measure
• Elliptic PDEs on Compact Ricci Limit Spaces and Applications
• Gaussian heat kernel upper bounds via the Phragmén-Lindelöf theorem
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
• Harmonic Forms and Heat Conduction
• Compactness of Schrödinger semigroups
• Optimal Transport
• Heat equation derivative formulas for vector bundles

This page was built for publication: Heat flow on 1-forms under lower Ricci bounds. Functional inequalities, spectral theory, and heat kernel