Higher genus Riemann minimal surfaces
Differential Geometry
2007-05-23 v1
Abstract
We construct higher genus Riemann's minimal surfaces properly embedded in the Euclidean space. To do that we glue end by end a Costa-Hoffman-Meeks examples to two halves genus zero Riemann's minimal surfaces. In first we need to perform a deformation of a Costa-Hoffman-Meeks example to prescribe the flux vector along the catenoidal ends. Then we study the mapping property of the Jacobi operator on the half Riemann example as a perturbation analysis of a CMC-Delaunay half cylinder.
Cite
@article{arxiv.math/0511438,
title = {Higher genus Riemann minimal surfaces},
author = {Laurent Hauswirth and Frank Pacard},
journal= {arXiv preprint arXiv:math/0511438},
year = {2007}
}
Comments
43 pages