Backwards uniqueness of the mean curvature flow

Details Backwards uniqueness of the mean curvature flow Backwards uniqueness of the mean curvature flow

2009-07-06

arxiv.org/abs/0907.0862v1

Mathematics

Differential Geometry

4 pages

Scientific paper

In this note we prove the backwards uniqueness of the mean curvature flow in codimension one case. More precisely,let $F_t, \widetilde{F}_t:M^n \to \overline{M}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n \times [0,T]$ with bounded second fundamental form in a complete ambient manifold with bounded geometry. Suppose $F_T=\widetilde{F}_T$, then $F_t=\widetilde{F}_t$ on $M^n \times [0,T]$. This is an analog of a recent result of Kotschwar on Ricci flow.

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