Hamilton’s gradient estimate for the heat kernel on complete manifolds

DOI10.1090/S0002-9939-07-08837-5zbMath1127.58021arXivmath/0701335WikidataQ125895569 ScholiaQ125895569MaRDI QIDQ5291949

Brett Kotschwar

Publication date: 19 June 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701335

zbMATH Keywords

Heat kernelGradient estimateComplete manifold

Mathematics Subject Classification ID

Heat equation (35K05) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (39)

Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below ⋮ Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below ⋮ Gradient estimates for a weighted nonlinear parabolic equation ⋮ Hamilton type gradient estimates for a general type of nonlinear parabolic equations on Riemannian manifolds ⋮ Local derivative estimates for the heat equation coupled to the Ricci flow ⋮ Besov class via heat semigroup on Dirichlet spaces. II: BV functions and Gaussian heat kernel estimates ⋮ Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability ⋮ Codimension four regularity of generalized Einstein structures ⋮ Elliptic gradient estimates for a nonlinear equation with Dirichlet boundary condition ⋮ Hamilton's gradient estimates and a monotonicity formula for heat flows on metric measure spaces ⋮ A generalization of Hamilton's gradient estimate ⋮ Logarithmic heat kernel estimates without curvature restrictions ⋮ Gradient estimates for a weighted \(\Gamma\)-nonlinear parabolic equation coupled with a super Perelman-Ricci flow and implications ⋮ Convergence of fundamental solutions of linear parabolic equations under Cheeger-Gromov convergence ⋮ Matrix Li-Yau-Hamilton estimates under Ricci flow and parabolic frequency ⋮ Gradient estimates for porous medium and fast diffusion equations by martingale method ⋮ Unnamed Item ⋮ Li-Yau-Hamilton estimates and Bakry-Emery-Ricci curvature ⋮ Elliptic gradient estimates for a parabolic equation with \(V\)-Laplacian and applications ⋮ \(L^2\) curvature bounds on manifolds with bounded Ricci curvature ⋮ On Li-Yau heat kernel estimate ⋮ Liouville theorems for ancient caloric functions via optimal growth conditions ⋮ Hamilton’s gradient estimates and Liouville theorems for fast diffusion equations on noncompact Riemannian manifolds ⋮ Perelman's entropy on ancient Ricci flows ⋮ Elliptic gradient estimates for a nonlinear heat equation and applications ⋮ Hamilton type gradient estimate for the sub-elliptic operators ⋮ A formula for the time derivative of the entropic cost and applications ⋮ Gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces ⋮ Gradient estimates and Harnack inequalities for a Yamabe-type parabolic equation under the Yamabe flow ⋮ Hamilton's Harnack inequality and the \(W\)-entropy formula on complete Riemannian manifolds ⋮ Gradient estimates and Harnack inequalities for a nonlinear parabolic equation on smooth metric measure spaces ⋮ Localized elliptic gradient estimate for solutions of the heat equation on \({ RCD}^\ast(K,N)\) metric measure spaces ⋮ Local parabolic and elliptic gradient estimates for a generalized heat-type equation under the Yamabe flow ⋮ Local elliptic gradient estimates for a nonlinear parabolic equation under the Ricci flow ⋮ Hamilton's gradient estimates for a nonlinear partial differential equation under the Yamabe flow ⋮ Gradient and Hessian estimates for an elliptic equation on smooth metric measure spaces ⋮ Sharp Hamilton’s Laplacian estimate for the heat kernel on complete manifolds ⋮ Gradient estimates for a general type of nonlinear parabolic equations under geometric conditions and related problems ⋮ Elliptic gradient estimates for a weighted heat equation and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Kähler-Ricci flow and the Poincaré-Lelong equation
• An extension of E. Hopf's maximum principle with an application to Riemannian geometry
• A note on Perelman's LYH-type inequality
• A gradient estimate for all positive solutions of the conjugate heat equation under Ricci flow
• On the parabolic kernel of the Schrödinger operator
• Deforming the metric on complete Riemannian manifolds
• A matrix Harnack estimate for the heat equation
• Addenda to ``The entropy formula for linear heat equation
• SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS

This page was built for publication: Hamilton’s gradient estimate for the heat kernel on complete manifolds