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Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds

Brian Dean
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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.

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Brian Dean. 2003-08-22. Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds. https://arxiv.org/abs/math/0308215

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