Matrix Li-Yau-Hamilton Estimates under Kähler-Ricci Flow

2023/07/20 by Xiaolong Li, Li, Xiaolong, Hao-Yue Liu +3 · 1 citation
Mathematics · #35K05 #53E30 #58J35 #Algebraic Geometry and Number Theory #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2307.10920

openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove matrix Li-Yau-Hamilton estimates for positive solutions to the heat equation and the backward conjugate heat equation, both coupled with the Kähler-Ricci flow. As an application, we obtain a monotonicity formula.

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• Backward Harnack inequality and Hamilton estimates for heat type equations

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