Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds

Details Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds Compact Embedded Minimal Surfaces of Positive Genus Without Area Bounds

2003-08-22

arxiv.org/abs/math/0308215v1

Mathematics

Differential Geometry

8 pages, 2 figures, to appear in Geomitrae Dedicata

Scientific paper

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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