Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds

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.

8 pages, 2 figures, to appear in Geomitrae Dedicata

References in corpus (1)

• The space of embedded minimal surfaces of fixed genus in a 3-manifold IV; Locally simply connected