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# Communications in Analysis and Geometry

## Volume 30 (2022)

### Number 5

### The Calderón problem for the conformal Laplacian

Pages: 1121 – 1184

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n5.a6

#### Authors

#### 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 [**LU02**, Conjecture 6.3]. 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.

Received 15 June 2018

Accepted 16 October 2019

Published 17 March 2023