Spacelike mean curvature flow

TL;DR

This paper establishes long-term existence and convergence of spacelike mean curvature flow solutions in pseudo-Euclidean space, with applications to G2-Laplacian flow in coassociative fibrations.

Contribution

It provides new long-time existence and convergence results for spacelike mean curvature flow and applies these to G2-Laplacian flow in specific geometric contexts.

Findings

Proves long-time existence of spacelike mean curvature flow solutions.

Demonstrates convergence of the flow under certain conditions.

Applies results to G2-Laplacian flow in coassociative fibrations.

Abstract

We prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space $\mathbb{R}^{n,m}$, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove long-time existence and convergence of the $\operatorname{G}_2$-Laplacian flow in cases related to coassociative fibrations.