An inverse problem for the Riemannian minimal surface equation

Cătălin I. Cârstea*, Matti Lassas, Tony Liimatainen, Lauri Oksanen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we consider determining a minimal surface embedded in a Riemannian manifold Σ×R. We show that if Σ is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine Σ up to an isometry.

Original languageEnglish
Pages (from-to)626-648
Number of pages23
JournalJournal of Differential Equations
Volume379
DOIs
StatePublished - 15 Jan 2024

Keywords

  • Higher order linearization
  • Inverse problems
  • Minimal surface
  • Quasilinear elliptic equation
  • Riemannian manifold
  • Riemannian surface

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