The Calderón problem for the conformal Laplacian
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
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
International Press
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202303292296Use this for linking
Review status
Peer reviewed
ISSN
1019-8385
DOI
https://doi.org/10.4310/cag.2022.v30.n5.a6
Language
English
Published in
Communications in Analysis and Geometry
Citation
- Lassas, M., Liimatainen, T., & Salo, M. (2022). The Calderón problem for the conformal Laplacian. Communications in Analysis and Geometry, 30(5), 1121-1184. https://doi.org/10.4310/cag.2022.v30.n5.a6
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Copyright© International Press