Complete minimal surfaces derived from Chen–Gackstatter genus two example

F.J. López, F. Martín and D. Rodríguez

Vol. 184 (1998), No. 2, 311–332

DOI: 10.2140/pjm.1998.184.311

Abstract

In this paper we present a family of complete minimal surfaces in ℝ³ with one end, arbitrary even genus k, 4k symmetries and total curvature −4π(2k − 1). Furthermore if k≠6 they are the only examples satisfying these conditions. If k = 2 our construction leads to the Chen–Gackstatter genus two surface.

Milestones

Received: 11 November 1996

Revised: 10 April 1997

Published: 1 June 1998