Sharp gradient estimates for a heat equation in Riemannian manifolds
From MaRDI portal
Publication:5238112
DOI10.1090/proc/14645zbMath1428.58021arXiv1810.03189OpenAlexW2963756381WikidataQ115290761 ScholiaQ115290761MaRDI QIDQ5238112
Nguyen Thac Dung, Ha Tuan Dung
Publication date: 28 October 2019
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.03189
Heat equation (35K05) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
Related Items
Gradient estimates for weighted \(p\)-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds ⋮ Gradient estimates for a nonlinear parabolic equation with Dirichlet boundary condition ⋮ Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian on noncompact Riemannian manifolds ⋮ Gradient estimates for a class of elliptic and parabolic equations on Riemannian manifolds ⋮ Local Hessian estimates of solutions to nonlinear parabolic equations along Ricci flow ⋮ Unnamed Item ⋮ Upper bounds of Hessian matrix and gradient estimates of positive solutions to the nonlinear parabolic equation along Ricci flow ⋮ Harnack inequality, heat kernel bounds and eigenvalue estimates under integral Ricci curvature bounds ⋮ Yau type gradient estimates for \(\Delta u + au (\log u)^p + bu = 0\) on 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 ⋮ Gradient estimates for a class of semilinear parabolic equations and their applications ⋮ Sharp gradient estimates on weighted manifolds with compact boundary ⋮ Global gradient estimates for a general type of nonlinear parabolic equations ⋮ Gradient estimates for a general type of nonlinear parabolic equations under geometric conditions and related problems ⋮ Liouville type theorems and gradient estimates for nonlinear heat equations along ancient \(K\)-super Ricci flow via reduced geometry
Cites Work
- Li-Yau-Hamilton estimates and Bakry-Emery-Ricci curvature
- Elliptic gradient estimates for a nonlinear heat equation and applications
- An extension of E. Hopf's maximum principle with an application to Riemannian geometry
- Comparison geometry for the Bakry-Emery Ricci tensor
- Gradient estimates and Liouville type theorems for a nonlinear elliptic equation
- On the parabolic kernel of the Schrödinger operator
- A matrix Harnack estimate for the heat equation
- Gradient estimates for some \(f\)-heat equations driven by Lichnerowicz's equation on complete smooth metric measure spaces
- A Liouville-type theorem for smooth metric measure spaces
- Elliptic gradient estimates for a weighted heat equation and applications
- Gradient estimate for a nonlinear heat equation on Riemannian manifolds
- SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
- On Ancient Solutions of the Heat Equation
