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arXiv · 1612.07939

The Calderón problem for the conformal Laplacian

Matti Lassas·Tony Liimatainen·Mikko Salo
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Abstract

We consider a conformally invariant version of the Calderón problem, where the objective is to determine the conformal class of a Riemannian manifold with boundary from the Dirichlet-to-Neumann map for the conformal Laplacian. The main result states that a locally conformally real-analytic manifold in dimensions $\geq 3$ can be determined in this way, giving a positive answer to an earlier conjecture by Lassas and Uhlmann (2001). The proof proceeds as in the standard Calderón problem on a real-analytic Riemannian manifold, but new features appear due to the conformal structure. In particular, we introduce a new coordinate system that replaces harmonic coordinates when determining the conformal class in a neighborhood of the boundary.

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Matti Lassas, Tony Liimatainen, Mikko Salo. 2016-12-23. The Calderón problem for the conformal Laplacian. https://arxiv.org/abs/1612.07939

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