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<p>Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [<CitationRef CitationID="CR1">1</CitationRef>], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.</p>

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Hamilton Type Gradient Estimates for a Heat Equation under the Ricci-harmonic Flow

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Liang-Chu Chang,
  • Nguyen Thac Dung,
  • Chiung-Jue Anna Sung

摘要

Our aim in this paper is to study the linear heat equation on a Riemannian manifold evolving by the Ricci-harmonic flow. We first show a Hamilton type gradient estimate for the positive solution of the heat equation, which allows us to derive a Harnack inequality. It is worthy to note that comparing with the Li-Yau type estimate by Bailesteanu [1], our gradient estimate can be obtained without any assumption on the harmonic quantity in the flow.