Li-Yau multiplier set and optimal Li-Yau gradient estimate on hyperbolic spaces

2018/07/16 by Chengjie Yu, Feifei Zhao, Yu, Chengjie +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1807.05709

openalex publication_date 2018/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, motivated by finding sharp Li-Yau type gradient estimate for positive solution of heat equations on complete Riemannian manifolds with negative Ricci curvature lower bound, we first introduce the notion of Li-Yau multiplier set and show that it can be computed by heat kernel of the manifold. Then, an optimal Li-Yau type gradient estimate is obtained on hyperbolic spaces by using recurrence relations of heat kernels on hyperbolic spaces. Finally, as an application, we obtain sharp Harnack inequalities on hyperbolic spaces.

Citations

• On the parabolic kernel of the Schrödinger operator

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• Some aspects of Cheng-Yau gradient estimates

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