Backwards uniqueness of the mean curvature flow

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 $F_t,{\tilde{F}}_t:M^n\to {\mathbb{R}}^{n+1}$ be two complete solutions of the mean curvature flow on $M^n\times [0,T]$ with bounded second fundamental forms. Suppose $F_T={\tilde{F}}_T$, then $F_t={\tilde{F}}_t$ on $M^n\times [0,T]$. This is an analog of a result of Kotschwar on the Ricci flow.

to appear in Geometriae Dedicata

References in corpus (3)

• Backwards uniqueness of the Ricci flow
• Note on the backwards uniqueness of mean curvature flow
• Uniqueness Theorem for non-compact mean curvature flow with possibly unbounded curvatures

Cited by in corpus (2)

• Gradient estimates and parabolic frequency under the Laplacian G_2 flow
• Backward Uniqueness of Extrinsic Geometric Flow in general ambient manifolds