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arXiv · 2203.09262

An inverse problem for the Riemannian minimal surface equation

Cătălin I. Cârstea·Matti Lassas·Tony Liimatainen·Lauri Oksanen
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Abstract

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

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Cătălin I. Cârstea, Matti Lassas, Tony Liimatainen, Lauri Oksanen. 2022-03-17. An inverse problem for the Riemannian minimal surface equation. https://arxiv.org/abs/2203.09262

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