scholarly journals The isoperimetric inequality for multiply-connected minimal surfaces

1965 ◽  
Vol 160 (5) ◽  
pp. 370-375 ◽  
Author(s):  
Johannes C. C. Nitsche
Keyword(s):  
Isoperimetric Inequality ◽  
Minimal Surfaces ◽  
Multiply Connected

The isoperimetric inequality for minimal surfaces in a Riemannian manifold

1999 ◽  
Vol 1999 (506) ◽  
pp. 205-214 ◽  
Author(s):  
Jaigyoung Choe
Keyword(s):  
Riemannian Manifold ◽  
Minimal Surface ◽  
Sectional Curvature ◽  
Isoperimetric Inequality ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Constant Gaussian Curvature ◽  
Simply Connected

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.

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