A1 Journal article (refereed)
Limiting Carleman weights and conformally transversally anisotropic manifolds (2020)

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

JYU authors or editors

Salo, Mikko

Publication details

All authors or editors: Angulo, Pablo; Faraco, Daniel; Guijarro, Luis; Salo, Mikko

Journal or series: Transactions of the American Mathematical Society

ISSN: 0002-9947

eISSN: 1088-6850

Publication year: 2020

Volume: 373

Issue number: 7

Pages range: 5171-5197

Publisher: American Mathematical Society

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1090/tran/8072

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/77415

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1811.02346

Abstract

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.

Keywords: partial differential equations; inverse problems; differential geometry; manifolds (mathematics)

Fields of science: