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<p>In this paper we are concerned with the matrix Li–Yau–Hamilton estimates for nonlinear parabolic equations. Firstly, we derive such estimate on a Riemannian manifold. Similar estimate on Kähler manifold with a fixed Kähler metric is obtained. Finally we consider the estimates on Kähler manifolds with Kähler metrics evolving under the Kähler–Ricci flow.</p>

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Matrix Li–Yau–Hamilton Estimates for Nonlinear Parabolic Equations

  • 期刊论文

  • 发表日期：

    2025年3月27日

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  • Pang Xu,
  • Hao-Yue Liu,
  • Xin-An Ren

摘要

In this paper we are concerned with the matrix Li–Yau–Hamilton estimates for nonlinear parabolic equations. Firstly, we derive such estimate on a Riemannian manifold. Similar estimate on Kähler manifold with a fixed Kähler metric is obtained. Finally we consider the estimates on Kähler manifolds with Kähler metrics evolving under the Kähler–Ricci flow.