Limiting Carleman weights and conformally transversally anisotropic manifolds
Angulo, P., Faraco, D., Guijarro, L., & Salo, M. (2020). Limiting Carleman weights and conformally transversally anisotropic manifolds. Transactions of the American Mathematical Society, 373(7), 5171-5197. https://doi.org/10.1090/tran/8072
Published inTransactions of the American Mathematical Society
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2020 American Mathematical Society
We analyze the structure of the set of limiting Carleman weights in all conformally flat manifolds, $ 3$-manifolds, and $ 4$-manifolds. In particular we give a new proof of the classification of Euclidean limiting Carleman weights, and show that there are only three basic such weights up to the action of the conformal group. In dimension three we show that if the manifold is not conformally flat, there could be one or two limiting Carleman weights. We also characterize the metrics that have more than one limiting Carleman weight. In dimension four we obtain a complete spectrum of examples according to the structure of the Weyl tensor. In particular, we construct unimodular Lie groups whose Weyl or Cotton-York tensors have the symmetries of conformally transversally anisotropic manifolds, but which do not admit limiting Carleman weights.
PublisherAmerican Mathematical Society
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Related funder(s)Academy of Finland; European Commission
Funding program(s)Centre of Excellence, AoF; Academy Project, AoF
The content of the publication reflects only the author’s view. The funder is not responsible for any use that may be made of the information it contains.
Additional information about fundingThe first author was supported by research grant MTM2017-85934-C3-3-P from the Ministerio de Ciencia e Innovación (MCINN) and ERC 301179. The second and third authors were supported by research grants MTM2014-57769-1-P, MTM2014- 57769-3-P, MTM2017-85934-C3-2-P from MCINN, by ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554 (MINECO), by ERC 301179 and by ERC 34728. The fourth author was supported by the Academy of Finland (grants 284715 and 309963) and by ERC under Horizon 2020 (ERC CoG 770924). ...
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