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arXiv · 2608.10541

Correspondence between Mean Curvature Flow and Harmonic-Ricci Flow

Tianyin Ren·Chong Song
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Abstract

In this paper, we observe that the (spacelike) mean curvature flow of a submanifold in a (pseudo-)Euclidean space is equivalent to a harmonic-Ricci flow with coupling constant $\alpha=-1$ (or $+1$), for the corresponding Gauss map and the induced metric. The solitons of these two flows are also equivalent. As an application, we get a monotonicity formula for the spacelike mean curvature flow.

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Tianyin Ren, Chong Song. 2026-08-11. Correspondence between Mean Curvature Flow and Harmonic-Ricci Flow. https://arxiv.org/abs/2608.10541

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