Constrained matrix Li-Yau-Hamilton estimates on K\"ahler manifolds
Xin-An Ren, Sha Yao, Li-Ju Shen, Guang-Ying Zhang
TL;DR
This paper develops new constrained matrix Li-Yau-Hamilton estimates for heat equations on K"ahler manifolds, including fixed and evolving metrics, advancing geometric analysis techniques.
Contribution
It introduces an interpolation version of the estimate and applies it to both fixed and evolving K"ahler metrics under Ricci flow.
Findings
Established constrained matrix Li-Yau-Hamilton estimate for heat equation on fixed K"ahler manifolds.
Derived estimate for conjugate heat equation under K"ahler-Ricci flow.
Extended the estimate to time-dependent K"ahler metrics.
Abstract
We derive an interpolation version of constrained matrix Li-Yau-Hamilton estimate on K\"ahler manifolds. As a result, we first get a constrained matrix Li-Yau-Hamilton estimate for heat equation on a K\"ahler manifold with fixed K\"ahler metric. Secondly, we get a corresponding estimate for forward conjugate heat equation on K\"ahler manifolds with time dependent K\"ahler metrics evolving by K\"ahler-Ricci flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research