Geometric relations of stable minimal surfaces and applications

Details Geometric relations of stable minimal surfaces and applications Geometric relations of stable minimal surfaces and applications

2010-02-17

arxiv.org/abs/1002.3274v1

Mathematics

Differential Geometry

25 pages; 3 figures

Scientific paper

We establish some a priori geometric relations on stable minimal surfaces lying inside three-manifolds with scalar curvature uniformly bounded below. The relations are based on a slight generalization of a formula due to Castillon. We apply it to prove non-local rigidity results in the particular sense that they express how local isoperimetric properties in some region affect the local isoperimetric properties in any other region. We present applications to understand the notion of isoperimetric collapse on three-manifolds with scalar curvature uniformly bounded below.

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