Open Access
February 2010 Adding one handle to half-plane layers
Laurent Mazet
J. Differential Geom. 84(2): 389-407 (February 2010). DOI: 10.4310/jdg/1274707318


In this paper, we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by their period. These surfaces are constructed by adding a handle to the toroidal half-plane layers defined by H. Karcher. The technics that we use are to solve a Jenkins-Serrin problem over a strip domain and to consider the conjugate minimal surface to the graph. To construct the Jenkins Serrin graph, we solve in fact the maximal surface equation and use an other conjugation technic.


Download Citation

Laurent Mazet. "Adding one handle to half-plane layers." J. Differential Geom. 84 (2) 389 - 407, February 2010.


Published: February 2010
First available in Project Euclid: 24 May 2010

zbMATH: 1194.53009
MathSciNet: MR2652466
Digital Object Identifier: 10.4310/jdg/1274707318

Rights: Copyright © 2010 Lehigh University

Vol.84 • No. 2 • February 2010
Back to Top