An inverse problem for the minimal surface equation in the presence of a riemannian metric
Nurminen, J. (2024). An inverse problem for the minimal surface equation in the presence of a riemannian metric. Nonlinearity, 37(9), Article 095029. https://doi.org/10.1088/1361-6544/ad6949
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© 2024 IOP Publishing Ltd & London Mathematical Society
In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold (R-n, g) where the metric is of the form g(x) = c(x)((g) over cap circle plus e). Here g<^> is a simple Riemannian metric on Rn-1, e is the Euclidean metric on R and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and c similar to g agree, then the Taylor series of the conformal factor c similar to at x(n) = 0 is equal to a positive constant. We also show a partial data result when n = 3.
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The author was supported by the Finnish Centre of Excellence in Inverse Modelling and Imaging (Academy of Finland Grant 284715) and by the Research Council of Finland (Flagship of Advanced Mathematics for Sensing Imaging and Modelling grant 359208)License
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