Revisiting Li-Yau type inequalities on Riemannian manifolds
Bin Qian
TL;DR
This paper presents a new version of Li-Yau gradient estimates for the heat equation on Riemannian manifolds, generalizing previous results and clarifying their interrelations.
Contribution
It introduces a generalized Li-Yau gradient estimate that unifies and extends existing inequalities on Riemannian manifolds.
Findings
New Li-Yau gradient estimate for the heat equation
Unification of known results as special cases
Extension of gradient estimates to broader settings
Abstract
Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the different known results as different cases here.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Numerical methods in inverse problems