Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Limiting Carleman weights and conformally transversally anisotropic manifolds


Authors: Pablo Angulo, Daniel Faraco, Luis Guijarro and Mikko Salo
Journal: Trans. Amer. Math. Soc. 373 (2020), 5171-5197
MSC (2010): Primary 35R30, 53A30; Secondary 58J32
DOI: https://doi.org/10.1090/tran/8072
Published electronically: April 29, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 35R30, 53A30, 58J32

Retrieve articles in all journals with MSC (2010): 35R30, 53A30, 58J32


Additional Information

Pablo Angulo
Affiliation: Department of Mathematics, ETS de Ingenieros Navales, Universidad Politécnica de Madrid, Spain
Email: pablo.angulo@upm.es

Daniel Faraco
Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain; and ICMAT CSIC-UAM-UCM-UC3M, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain
Email: daniel.faraco@uam.es

Luis Guijarro
Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain; and ICMAT CSIC-UAM-UCM-UC3M, Ciudad Universitaria de Cantoblanco, 28049 Madrid, Spain
Email: luis.guijarro@uam.es

Mikko Salo
Affiliation: Department of Mathematics and Statistics, University of Jyvaskyla, P.O. Box 35, 40014 University of Jyvaskyla, Finland
Email: mikko.j.salo@jyu.fi

DOI: https://doi.org/10.1090/tran/8072
Received by editor(s): November 28, 2018
Received by editor(s) in revised form: December 6, 2019
Published electronically: April 29, 2020
Additional Notes: The 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).
Article copyright: © Copyright 2020 American Mathematical Society