Area minimization among marginally trapped surfaces in Lorentz-Minkowski space

TL;DR

This paper investigates the problem of minimizing the area of spacelike zero mean curvature surfaces in Lorentz-Minkowski space by comparing them with marginally trapped surfaces sharing the same boundary.

Contribution

It introduces an area minimization framework for spacelike zero mean curvature surfaces and compares their areas with marginally trapped surfaces in Lorentz-Minkowski space.

Findings

Zero mean curvature surfaces can be compared to marginally trapped surfaces with the same boundary.

The study establishes conditions under which area minimization occurs.

Results contribute to understanding geometric properties of surfaces in Lorentzian manifolds.

Abstract

We study an area minimization problem for spacelike zero mean curvature surfaces in four dimensional Lorentz-Minkowski space. The areas of these surfaces are compared of with the areas of certain marginally trapped surfaces having the same boundary values.