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<p>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. These estimates are further extended to the constrained setting. As an application, we obtain a monotonicity formula.</p>

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Matrix Li–Yau–Hamilton Estimates Under Kähler–Ricci Flow

  • 期刊论文

  • 发表日期：

    2025年2月28日

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

摘要

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. These estimates are further extended to the constrained setting. As an application, we obtain a monotonicity formula.