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

Shoichi Fujimori and Toshihiro Shoda

Vol. 282 (2016), No. 1, 107–144

DOI: 10.2140/pjm.2016.282.107

Abstract

We consider complete noncatenoidal minimal surfaces of finite total curvature with two ends. A family of such minimal surfaces with least total absolute curvature is given. We also obtain a uniqueness theorem for this family from its symmetries.

Keywords

minimal surface, finite total curvature, two ends

Mathematical Subject Classification 2010

Primary: 53A10

Secondary: 49Q05, 53C42

Milestones

Received: 1 April 2015

Accepted: 12 September 2015

Published: 24 February 2016