Asymptotically flat three-manifolds contain minimal planes

Otis Chodosh; Daniel Ketover

doi:10.1016/j.aim.2018.08.010

Asymptotically flat three-manifolds contain minimal planes

Otis Chodosh
, Daniel Ketover

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

7 Scopus citations

Abstract

Let (M,g) be an asymptotically flat 3-manifold containing no closed embedded minimal surfaces. We prove that for every point p∈M there exists a complete properly embedded minimal plane in M containing p.

Original language	English (US)
Pages (from-to)	171-192
Number of pages	22
Journal	Advances in Mathematics
Volume	337
DOIs	https://doi.org/10.1016/j.aim.2018.08.010
State	Published - Oct 15 2018

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Asymptotically flat manifolds
Degree theory
Minimal surfaces

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10.1016/j.aim.2018.08.010

Cite this

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title = "Asymptotically flat three-manifolds contain minimal planes",

abstract = "Let (M,g) be an asymptotically flat 3-manifold containing no closed embedded minimal surfaces. We prove that for every point p∈M there exists a complete properly embedded minimal plane in M containing p.",

keywords = "Asymptotically flat manifolds, Degree theory, Minimal surfaces",

author = "Otis Chodosh and Daniel Ketover",

note = "Publisher Copyright: {\textcopyright} 2018",

year = "2018",

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doi = "10.1016/j.aim.2018.08.010",

language = "English (US)",

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T1 - Asymptotically flat three-manifolds contain minimal planes

AU - Chodosh, Otis

AU - Ketover, Daniel

PY - 2018/10/15

Y1 - 2018/10/15

N2 - Let (M,g) be an asymptotically flat 3-manifold containing no closed embedded minimal surfaces. We prove that for every point p∈M there exists a complete properly embedded minimal plane in M containing p.

AB - Let (M,g) be an asymptotically flat 3-manifold containing no closed embedded minimal surfaces. We prove that for every point p∈M there exists a complete properly embedded minimal plane in M containing p.

KW - Asymptotically flat manifolds

KW - Degree theory

KW - Minimal surfaces

UR - https://www.scopus.com/pages/publications/85054054824

UR - https://www.scopus.com/pages/publications/85054054824#tab=citedBy

U2 - 10.1016/j.aim.2018.08.010

DO - 10.1016/j.aim.2018.08.010

M3 - Article

AN - SCOPUS:85054054824

SN - 0001-8708

VL - 337

SP - 171

EP - 192

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Asymptotically flat three-manifolds contain minimal planes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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