Scherk Saddle Towers of Genus Two in $\R^3$
Differential Geometry
2009-06-09 v1
Abstract
In 1996 M. Traizet obtained singly periodic minimal surfaces with Scherk ends of arbitrary genus by desingularizing a set of vertical planes at their intersections. However, in Traizet's work it is not allowed that three or more planes intersect at the same line. In our paper, by a {\it saddle-tower} we call the desingularization of such ``forbidden'' planes into an embedded singly periodic minimal surface. We give explicit examples of genus two and discuss some advances regarding this problem. Moreover, our examples are the first ones containing {\it Gaussian geodesics}, and for the first time we prove embeddedness of the surfaces CSSCFF and CSSCCC from Callahan-Hoffman-Meeks-Wohlgemuth.
Keywords
Cite
@article{arxiv.0906.1546,
title = {Scherk Saddle Towers of Genus Two in $\R^3$},
author = {M. F. da Silva and V. Ramos Batista},
journal= {arXiv preprint arXiv:0906.1546},
year = {2009}
}