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

Simon Brendle; Pei Ken Hung

doi:10.1007/s00039-017-0399-6

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

Simon Brendle
, Pei Ken Hung

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 language	English (US)
Pages (from-to)	235-239
Number of pages	5
Journal	Geometric and Functional Analysis
Volume	27
Issue number	2
DOIs	https://doi.org/10.1007/s00039-017-0399-6
State	Published - Apr 1 2017
Externally published	Yes

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© 2017, Springer International Publishing.

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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.",

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N2 - 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.

AB - 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.

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JO - Geometric and Functional Analysis

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ER -

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

Abstract

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