Li-Yau gradient estimates on closed manifolds under bakry-emery ricci curvature conditions

TL;DR

This paper establishes Li-Yau gradient estimates for positive solutions of the f-heat equation on closed manifolds with Bakry-Emery Ricci curvature bounds, extending previous results in geometric analysis.

Contribution

It provides new gradient bounds under Bakry-Emery Ricci curvature conditions, generalizing classical Li-Yau estimates to weighted manifolds.

Findings

Derived Li-Yau gradient bounds for f-heat equations

Extended classical estimates to Bakry-Emery Ricci curvature settings

Applicable to closed manifolds with curvature lower bounds

Abstract

In this paper, motivated by the work of Qi S. Zhang in [28], we derive Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Emery Ricci curvature bounded below.