Matrix Li-Yau-Hamilton Estimates under K\"ahler-Ricci Flow

Author:

Xiaolong Li, Hao-Yue Liu, Xin-An Ren

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

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date:

2023-07-19 16:00:00

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 K\"ahler-Ricci flow. As an application, we obtain a monotonicity formula.