Minimal surfaces with two ends which have the least total absolute curvature

TL;DR

This paper introduces a family of complete minimal surfaces with two ends that minimize total absolute curvature and proves their uniqueness based on symmetry properties.

Contribution

It provides a new family of minimal surfaces with least total absolute curvature and establishes a uniqueness theorem for this family.

Findings

Constructed a family of minimal surfaces with two ends and minimal total absolute curvature.

Proved a uniqueness theorem for these minimal surfaces based on their symmetries.

Abstract

In this paper, we consider complete non-catenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. Moreover, we obtain a uniqueness theorem for this family from its symmetries.