A sharp bound for the area of minimal surfaces in the unit ball

2011/08/23 by Brendle, S. · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1108.4544

Abstract

Let Σbe a k-dimensional minimal surface in the unit ball Bⁿ which meets the unit sphere orthogonally. We show that the area of Σis bounded from below by the volume of the unit ball in R^k. This answers a question posed by R. Schoen.

Cited by

• Evolution of hypersurfaces in (n+1)-dimensional light-cone
• Lengths of Orthogonal Geodesic Chords on Riemannian Manifolds

Related

• Area bounds for minimal surfaces that pass through a prescribed point in a ball
• Area Bounds for Free Boundary Minimal Surfaces in a Geodesic Ball in the\n Sphere
• Sharp Area Bounds for Free Boundary Minimal Surfaces in Conformally\n Euclidean Balls
• Area bounds for minimal surfaces in geodesic ball of hyperbolic space
• Area rigidity for the equatorial disk in the ball