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

TY - JOUR

T1 - Curvature estimates for minimal surfaces with total boundary curvature less than 4π

AU - Tinaglia, Giuseppe

PY - 2009/7

Y1 - 2009/7

N2 - 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.

AB - 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.

U2 - 10.1090/S0002-9939-09-09810-4

DO - 10.1090/S0002-9939-09-09810-4

M3 - Article

SN - 1088-6826

VL - 137

SP - 2445

EP - 2450

JO - PROCEEDINGS- AMERICAN MATHEMATICAL SOCIETY

JF - PROCEEDINGS- AMERICAN MATHEMATICAL SOCIETY

IS - 7

ER -