Construction of Maximal Hypersurfaces with Boundary Conditions

TL;DR

This paper develops a method to construct maximal hypersurfaces in Minkowski space using mean curvature flow, establishing conditions for long-term existence with boundary curvature assumptions.

Contribution

It introduces a new approach to construct maximal hypersurfaces with boundary conditions via mean curvature flow, including general existence criteria.

Findings

Established long-time existence conditions for the flow

Provided curvature assumptions for boundary manifolds

Constructed maximal hypersurfaces with prescribed boundary conditions

Abstract

We construct maximal hypersurfaces with a Neumann boundary condition in Minkowski space via mean curvature flow. In doing this we give general conditions for long time existence of the flow with boundary conditions with assumptions on the curvature of a the Lorentz boundary manifold.