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<p>This paper is concerned with the monotonicity of frequency function for solutions to the linear heat equation on Riemannian manifolds. As an application, we obtain a unique continuation result. We also derive the monotonicity of a new frequency function for solutions of the backward conjugate heat equation under the Ricci flow on surfaces.</p>

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Parabolic frequency monotonicity on compact Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Pang Xu,
  • Xin-An Ren

摘要

This paper is concerned with the monotonicity of frequency function for solutions to the linear heat equation on Riemannian manifolds. As an application, we obtain a unique continuation result. We also derive the monotonicity of a new frequency function for solutions of the backward conjugate heat equation under the Ricci flow on surfaces.