On the asymptotic Plateau problem for area minimizing surfaces in E(- 1 , τ)

Patrícia Klaser; Ana Menezes; Alvaro Ramos

doi:10.1007/s10455-020-09713-w

On the asymptotic Plateau problem for area minimizing surfaces in E(- 1 , τ)

Patrícia Klaser, Ana Menezes, Alvaro Ramos

Mathematics

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2 Scopus citations

Abstract

We prove some existence and nonexistence results for complete area minimizing surfaces in the homogeneous space E(- 1 , τ). As one of our main results, we present sufficient conditions for a curve Γ in ∂_∞E(- 1 , τ) to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in E(- 1 , τ) having Γ as its asymptotic boundary.

Original language	English (US)
Pages (from-to)	1-17
Number of pages	17
Journal	Annals of Global Analysis and Geometry
Volume	58
Issue number	1
DOIs	https://doi.org/10.1007/s10455-020-09713-w
State	Published - Jul 1 2020

All Science Journal Classification (ASJC) codes

Analysis
Political Science and International Relations
Geometry and Topology

Keywords

Area minimizing surfaces
Asymptotic Plateau problem
Asymptotic boundary
E(κ, τ) spaces

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abstract = "We prove some existence and nonexistence results for complete area minimizing surfaces in the homogeneous space E(- 1 , τ). As one of our main results, we present sufficient conditions for a curve Γ in ∂∞E(- 1 , τ) to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in E(- 1 , τ) having Γ as its asymptotic boundary.",

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AU - Menezes, Ana

AU - Ramos, Alvaro

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N2 - We prove some existence and nonexistence results for complete area minimizing surfaces in the homogeneous space E(- 1 , τ). As one of our main results, we present sufficient conditions for a curve Γ in ∂∞E(- 1 , τ) to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in E(- 1 , τ) having Γ as its asymptotic boundary.

AB - We prove some existence and nonexistence results for complete area minimizing surfaces in the homogeneous space E(- 1 , τ). As one of our main results, we present sufficient conditions for a curve Γ in ∂∞E(- 1 , τ) to admit a solution to the asymptotic Plateau problem, in the sense that there exists a complete area minimizing surface in E(- 1 , τ) having Γ as its asymptotic boundary.

KW - Area minimizing surfaces

KW - Asymptotic Plateau problem

KW - Asymptotic boundary

KW - E(κ, τ) spaces

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On the asymptotic Plateau problem for area minimizing surfaces in E(- 1 , τ)

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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