Timelike minimal surface in $\mathbb{E}^3_1$ with arbitrary ends

TL;DR

This paper proves the existence of timelike minimal surfaces in three-dimensional Minkowski space with any number of ends, analyzing their asymptotic behavior and singularity topology.

Contribution

It introduces a method to construct timelike minimal surfaces with arbitrary ends and studies their asymptotic and singularity properties.

Findings

Existence of timelike minimal surfaces with arbitrary ends.

Characterization of asymptotic behavior of simple ends.

Analysis of the topology of singularity sets.

Abstract

In this paper, we show the existence of a timelike minimal surface with an arbitrary number of weak complete ends. Then, we discuss the asymptotic behaviour of the simple ends and the topology of the singularity set of the constructed timelike minimal surface.