Correspondence between Mean Curvature Flow and Harmonic-Ricci Flow
Tianyin Ren, Chong Song
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 α=-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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