Spacelike mean curvature flow

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 $G_2$-Laplacian flow in cases related to coassociative fibrations.

This is a pre-print of an article published in The Journal of Geometric Analysis. The final authenticated version is available online at: https://doi.org/10.1007/s12220-019-00266-4

References in corpus (2)

• Hypersymplectic 4-manifolds, the $G_2$-Laplacian flow and extension assuming bounded scalar curvature
• Shi-type estimates and finite time singularities of flows of G${}_2$ structures

Cited by in corpus (4)

• $S^1$-invariant Laplacian flow
• Mean curvature flow in null hypersurfaces and the detection of MOTS
• A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
• Closed G${}_2$-structures on unimodular Lie algebras with non-trivial center