# Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension

## TL;DR

This paper proves the long-time existence of mean curvature flow for smooth spacelike submanifolds in higher codimension under certain curvature conditions, advancing understanding of geometric evolution in Lorentzian manifolds.

## Contribution

It establishes long-time existence results for mean curvature flow of spacelike submanifolds in higher codimension with timelike curvature conditions, a novel extension in Lorentzian geometry.

## Key findings

- Proves long-time existence under timelike curvature condition
- Extends mean curvature flow analysis to higher codimension
- Provides foundational results for geometric evolution in Lorentzian manifolds

## 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.