Geometric relations of stable minimal surfaces and applications

Martin Reiris

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arXiv · 1002.3274

Geometric relations of stable minimal surfaces and applications

Martin Reiris

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Abstract

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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Martin Reiris. 2010-02-17. Geometric relations of stable minimal surfaces and applications. https://arxiv.org/abs/1002.3274

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