On stability of the catenoid under vanishing mean curvature flow on Minkowski space

TL;DR

This paper investigates the stability of the catenoid minimal surface in Minkowski space under hyperbolic vanishing mean curvature flow, establishing local existence and stability for small perturbations.

Contribution

It provides the first stability analysis of the catenoid under hyperbolic mean curvature flow in Minkowski space, including local existence results.

Findings

Proved local existence of solutions near the catenoid

Established stability of the catenoid under small perturbations

Demonstrated the behavior of the flow in Minkowski space

Abstract

We establish basic local existence as well as a stability result concerning small perturbations of the Catenoid minimal surface in $\R^3$ under hyperbolic vanishing mean curvature flow.