Curvature estimates for minimal surfaces with total boundary curvature less than 4π

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Abstract

We establish a curvature estimate for classical minimal surfaces with total boundary curvature less than 4 pi. The main application is a bound on the genus of these surfaces depending solely on the geometry of the boundary curve. We also prove that the set of simple closed curves with total curvature less than 4 pi and which do not bound an orientable compact embedded minimal surface of genus greater than g, for any given g, is open in the C-2,C-alpha topology.

Original languageEnglish
Pages (from-to)2445-2450
Number of pages6
JournalPROCEEDINGS- AMERICAN MATHEMATICAL SOCIETY
Volume137
Issue number7
Early online date6 Feb 2009
DOIs
Publication statusPublished - Jul 2009

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