Parabolic frequency for the weighted heat equation under the Perelman's Ricci flow

Jianhong Wang

doi:10.4134/BKMS.b240394

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Parabolic frequency for the weighted heat equation under the Perelman's Ricci flow

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Ricci curvature Parabolic frequency weighted heat equation perelman's Ricci flow

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초록

The main purpose of this paper is to establish the monotonicity of parabolic frequency for the weighted heat equation on Riemannian manifolds with the metrics evolving by the Perelman's Ricci flow. We extend the related results of the heat equation coupled with the Ricci flow, which were studied in \cite{LLX22}. Compared with \cite{LLX22}, we only assume the weaker curvature conditions.

Abstract

The main purpose of this paper is to establish the monotonicity of parabolic frequency for the weighted heat equation on Riemannian manifolds with the metrics evolving by the Perelman's Ricci flow. We extend the related results of the heat equation coupled with the Ricci flow, which were studied in \cite{LLX22}. Compared with \cite{LLX22}, we only assume the weaker curvature conditions.

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