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The isoperimetric inequality for minimal surfaces in a Riemannian manifold
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Jaigyoung Choe
Published/Copyright:
June 11, 2008
Abstract
It is proved that every minimal surface with one or two boundary components in a simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant K satisfies the sharp isoperimetric inequality 4π A ≦ L2 + K A2. Here equality holds if and only if the minimal surface is a geodesic disk in a surface of constant Gaussian curvature K.
Received: 1998-04-21
Accepted: 1998-08-06
Published Online: 2008-06-11
Published in Print: 1999-01-15
© Walter de Gruyter
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- Projective normality and syzygies of algebraic surfaces
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Articles in the same Issue
- Le problème de Brill-Noether pour des fibrés stables de petite pente
- The affine curve-lengthening flow
- Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
- Analytic functions on Zariski open sets, and local cohomology
- Projective normality and syzygies of algebraic surfaces
- The outer derivation of a complex Poisson manifold
- Nevanlinna-Pick interpolation on the bidisk
- The isoperimetric inequality for minimal surfaces in a Riemannian manifold
- Values of symmetric square L-functions at 1
