Area Bounds for Minimal Surfaces that Pass Through a Prescribed Point in a Ball

Simon Brendle, Pei Ken Hung

Research output: Contribution to journalArticlepeer-review

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 |Bk|(1-|y|2)k2. This settles a question left open by the work of Alexander and Osserman in 1973.

Original languageEnglish (US)
Pages (from-to)235-239
Number of pages5
JournalGeometric and Functional Analysis
Volume27
Issue number2
DOIs
StatePublished - Apr 1 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing.

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