Singularities of axially symmetric time-like minimal submanifolds in Minkowski space

TL;DR

This paper proves the non-existence of global axisymmetric solutions for time-like minimal submanifolds in Minkowski space and analyzes their limiting geometry near maximal existence time.

Contribution

It establishes a non-existence result for global solutions and investigates the geometric behavior as solutions approach singularity.

Findings

No global-in-time axisymmetric solutions exist.

Analysis of the limiting geometry near maximal time.

Insights into singularity formation in Minkowski space.

Abstract

We prove that there does not exist global-in-time axisymmetric solutions to the time-like minimal submanifold system in Minkowski space. We further analyze the limiting geometry as the maximal time of existence is approached.