Hamilton differential Harnack inequality and \(W\)-entropy for Witten Laplacian on Riemannian manifolds

DOI10.1016/j.jfa.2017.09.017zbMath1386.53082arXiv1707.01644OpenAlexW2963634712WikidataQ125907410 ScholiaQ125907410MaRDI QIDQ1709726

Songzi Li, Xiang Dong Li

Publication date: 6 April 2018

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

Full work available at URL: https://arxiv.org/abs/1707.01644

zbMATH Keywords

\(W\)-entropyHamilton differential Harnack inequalitysuper Ricci flows

Mathematics Subject Classification ID

Related Items (20)

Elliptic gradient estimates for a nonlinear \(f\)-heat equation on weighted manifolds with evolving metrics and potentials ⋮ Local curvature estimates for the Ricci-harmonic flow ⋮ Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow ⋮ \(\mathcal{W}\)-entropy formulae and differential Harnack estimates for porous medium equations on Riemannian manifolds ⋮ Liouville theorem for heat equation Along ancient super Ricci flow via reduced geometry ⋮ \(W\)-entropy, super Perelman Ricci flows, and \((K, m)\)-Ricci solitons ⋮ Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with evolving metrics and potentials ⋮ Comparison geometry of manifolds with boundary under lower \(N\)-weighted Ricci curvature bounds with \(\varepsilon \)-range ⋮ Gradient estimates for a weighted \(\Gamma\)-nonlinear parabolic equation coupled with a super Perelman-Ricci flow and implications ⋮ New Laplacian comparison theorem and its applications to diffusion processes on Riemannian manifolds ⋮ Liouville theorem for \(V\)-harmonic maps under non-negative \((m, V)\)-Ricci curvature for non-positive \(m\) ⋮ \(W\)-entropy and Langevin deformation on Wasserstein space over Riemannian manifolds ⋮ Liouville theorems and elliptic gradient estimates for a nonlinear parabolic equation involving the Witten Laplacian ⋮ Monotonicity and rigidity of the \(\mathcal{W}\)-entropy on \(\mathsf{RCD} (0, N)\) spaces ⋮ Unnamed Item ⋮ \(W\)-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds ⋮ Some gradient estimates and Liouville properties of the fast diffusion equation on Riemannian manifolds ⋮ Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry ⋮ Laplacian comparison theorem on Riemannian manifolds with modified \(m\)-Bakry-Emery Ricci lower bounds for \(m\leq1\) ⋮ A note on Harnack type inequality for the Gaussian curvature flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Perelman's entropy formula for the Witten Laplacian on Riemannian manifolds via Bakry-Emery Ricci curvature
• The \(W\)-entropy formula for the Witten Laplacian on manifolds with time dependent metrics and potentials
• Differential Harnack inequalities on Riemannian manifolds. I: Linear heat equation
• Perelman's \(W\)-entropy for the Fokker-Planck equation over complete Riemannian manifolds
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• Comparison geometry for the Bakry-Emery Ricci tensor
• On the parabolic kernel of the Schrödinger operator
• A matrix Harnack estimate for the heat equation
• Some geometric properties of the Bakry-Émery-Ricci tensor
• The entropy formula for linar heat equation
• Super-Ricci flows for metric measure spaces
• \(W\)-entropy, super Perelman Ricci flows, and \((K, m)\)-Ricci solitons
• Liouville theorems for symmetric diffusion operators on complete Riemannian manifolds
• Heat Flow on Time‐Dependent Metric Measure Spaces and Super‐Ricci Flows
• Hamilton's Harnack inequality and the \(W\)-entropy formula on complete Riemannian manifolds

This page was built for publication: Hamilton differential Harnack inequality and \(W\)-entropy for Witten Laplacian on Riemannian manifolds