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

Patrícia Klaser, Ana Menezes, Alvaro Ramos

Research output: Contribution to journalArticle

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 languageEnglish (US)
JournalAnnals of Global Analysis and Geometry
Volume58
Issue number1
DOIs
StatePublished - 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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