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<p>This paper is devoted to the investigation of the monotonicity of parabolic frequency functional under conformal Ricci flow defined on a closed Riemannian manifold of constant scalar curvature and dimension not less than 3. Parabolic frequency functional for solutions of certain linear heat equation coupled with conformal pressure is defined and its monotonicity under the conformal Ricci flow is proved by applying Bakry-Émery Ricci curvature bounds. Some consequences of the monotonicity are also presented.</p>

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Parabolic frequency monotonicity on the conformal Ricci flow

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Abimbola Abolarinwa,
  • Shahroud Azami

摘要

This paper is devoted to the investigation of the monotonicity of parabolic frequency functional under conformal Ricci flow defined on a closed Riemannian manifold of constant scalar curvature and dimension not less than 3. Parabolic frequency functional for solutions of certain linear heat equation coupled with conformal pressure is defined and its monotonicity under the conformal Ricci flow is proved by applying Bakry-Émery Ricci curvature bounds. Some consequences of the monotonicity are also presented.