Explicit minimal Scherk saddle towers of arbitrary even genera in $\R^3$
Abstract
Starting from works by Scherk (1835) and by Enneper-Weierstra\ss \ (1863), new minimal surfaces with Scherk ends were found only in 1988 by Karcher (see \cite{Karcher1,Karcher}). In the singly periodic case, Karcher's examples of positive genera had been unique until Traizet obtained new ones in 1996 (see \cite{Traizet}). However, Traizet's construction is implicit and excludes {\it towers}, namely the desingularisation of more than two concurrent planes. Then, new explicit towers were found only in 2006 by Martin and Ramos Batista (see \cite{Martin}), all of them with genus one. For genus two, the first such towers were constructed in 2010 (see \cite{Valerio2}). Back to 2009, implicit towers of arbitrary genera were found in \cite{HMM}. In our present work we obtain {\it explicit} minimal Scherk saddle towers, for any given genus , .
Keywords
Cite
@article{arxiv.1308.5962,
title = {Explicit minimal Scherk saddle towers of arbitrary even genera in $\R^3$},
author = {A. J. Yucra Hancco and G. A. Lobos and V. Ramos Batista},
journal= {arXiv preprint arXiv:1308.5962},
year = {2013}
}