English

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.

Keywords

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

R2 v1 2026-07-22T16:57:07.308Z