An inverse problem for the Riemannian minimal surface equation

Catalin I. Carstea,Matti Lassas,Tony Liimatainen,Lauri Oksanen

JOURNAL OF DIFFERENTIAL EQUATIONS（2024）

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Abstract

In this paper we consider determining a minimal surface embedded in a Riemannian manifold E x R. We show that if E is a two dimensional Riemannian manifold with boundary, then the knowledge of the associated Dirichlet-to-Neumann map for the minimal surface equation determine E up to an isometry. (c) 2023 Elsevier Inc. All rights reserved.

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Key words

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

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