Vol. 282, No. 1, 2016

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

Shoichi Fujimori and Toshihiro Shoda

Vol. 282 (2016), No. 1, 107–144
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
Authors
Shoichi Fujimori
Department of Mathematics
Okayama University
Okayama 700-8530
Japan
Toshihiro Shoda
Faculty of Culture and Education
Saga University
1 Honjo-machi
Saga-city 840-8502
Japan