Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds
Differential Geometry
2007-05-23 v1
Abstract
Let M be a 3-manifold (possibly with boundary). We show that, for any positive integer g, there exists an open nonempty set of metrics on M for each of which there are stable compact embedded minimal surfaces of genus g with arbitrarily large area. This extends the result of Colding and Minicozzi for g=1.
Cite
@article{arxiv.math/0308215,
title = {Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds},
author = {Brian Dean},
journal= {arXiv preprint arXiv:math/0308215},
year = {2007}
}
Comments
8 pages, 2 figures, to appear in Geomitrae Dedicata