Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

Abstract

We prove long-time existence for mean curvature flow of a smooth $n$-dimensional spacelike submanifold of an $n+m$ dimensional manifold whose metric satisfies the timelike curvature condition.

19 pages LaTEX. Essentially this is Section 3 of the Proof of the Caratheodory Conjecture by the same authors, which is posted at arXiv:0808.0851

References in corpus (2)

• Self-shrinkers of the mean curvature flow in arbitrary codimension
• Global smooth geodesic foliations of the hyperbolic space

Cited by in corpus (1)

• From CT scans to 4-manifold topology