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

Research output: Contribution to journal › Article › peer-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 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

ASJC Scopus subject areas

Analysis
Geometry and Topology

Online availability

10.1007/s00039-017-0399-6

Library availability

Discover UIUC Full Text

Cite this

@article{dd06999e05d44eb4badb22d3a4a7fcd2,

title = "Area Bounds for Minimal Surfaces that Pass Through a Prescribed Point in a Ball",

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.",

author = "Simon Brendle and Hung, {Pei Ken}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing.",

year = "2017",

month = apr,

day = "1",

doi = "10.1007/s00039-017-0399-6",

language = "English (US)",

volume = "27",

pages = "235--239",

journal = "Geometric and Functional Analysis",

issn = "1016-443X",

publisher = "Birkhauser Verlag Basel",

number = "2",

}

TY - JOUR

T1 - Area Bounds for Minimal Surfaces that Pass Through a Prescribed Point in a Ball

AU - Brendle, Simon

AU - Hung, Pei Ken

PY - 2017/4/1

Y1 - 2017/4/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85013861368&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013861368&partnerID=8YFLogxK

U2 - 10.1007/s00039-017-0399-6

DO - 10.1007/s00039-017-0399-6

M3 - Article

AN - SCOPUS:85013861368

SN - 1016-443X

VL - 27

SP - 235

EP - 239

JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 2

ER -

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

Abstract

ASJC Scopus subject areas

Online availability

Library availability

Related links

Fingerprint

Cite this