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An inverse problem for the Riemannian minimal surface equation

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arxiv 2203.09262 v1 pith:USSTCD62 submitted 2022-03-17 math.AP math.DG

Cătălin I. Cârstea , Matti Lassas , Tony Liimatainen , Lauri Oksanen This is my paper
classification math.APmath.DG
keywords minimalriemanniansigmasurfaceequationmanifoldassociatedboundary
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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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  1. Partial data Calder\'{o}n problem for quasilinear conductivities in dimension 2

    math.AP 2026-07 conditional novelty 6.0 of 10

    Partial boundary measurements uniquely determine a quasilinear two-dimensional conductivity γ(x,u,∇u) without restricting the gradient dependence.

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