Area bounds for minimal surfaces that pass through a prescribed point in a ball

2016/07/15 by Brendle, S., Hung, P. K. · 1 citation
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1607.04631

Abstract

Let Σ be a k-dimensional minimal submanifold in the n-dimensional unit ball Bⁿ which passes through a point y ∈ Bⁿ and satisfies ∂ Σ⊂ ∂ Bⁿ. We show that the k-dimensional area of Σ is bounded from below by |B^k| (1-|y|²)^(k)/(2). This settles a question left open by the work of Alexander and Osserman in 1973.

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