Complete minimal surfaces of finite topology in the doubled Schwarzschild 3-manifold

TL;DR

This paper constructs complete embedded minimal surfaces of arbitrary genus within the doubled Schwarzschild 3-manifold using a classical desingularization method, expanding the understanding of minimal surfaces in this geometric setting.

Contribution

It introduces a novel construction of minimal surfaces of any genus in the doubled Schwarzschild 3-manifold via desingularization techniques.

Findings

Successfully constructs minimal surfaces of arbitrary genus.

Demonstrates the applicability of desingularization in this geometric context.

Provides new examples of minimal surfaces in the doubled Schwarzschild 3-manifold.

Abstract

We construct a complete embedded minimal surface with arbitrary genus in the doubled Schwarzschild 3-manifold. A classical desingularization method is used for the construction.