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arXiv · 0907.0862

Backwards uniqueness of the mean curvature flow

Hong Huang
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Abstract

In this note we prove the backwards uniqueness of the mean curvature flow for (codimension one) hypersurfaces in a Euclidean space. More precisely, let $F_t, \widetilde{F}_t:M^n \rightarrow \mathbb{R}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n \times [0,T]$ with bounded second fundamental forms. Suppose $F_T=\widetilde{F}_T$, then $F_t=\widetilde{F}_t$ on $M^n \times [0,T]$. This is an analog of a result of Kotschwar on the Ricci flow.

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Hong Huang. 2009-07-06. Backwards uniqueness of the mean curvature flow. https://doi.org/10.1007/s10711-019-00424-6

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