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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The conformal group of a compact simply connected Lorentzian manifold
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by Karin Melnick and Vincent Pecastaing HTML | PDF
J. Amer. Math. Soc. 35 (2022), 81-122 Request permission

Abstract:

We prove that the conformal group of a closed, simply connected, real analytic Lorentzian manifold is compact. D’Ambra proved in 1988 that the isometry group of such a manifold is compact [Invent. Math. 92 (1988), pp. 555–565]. Our result implies the Lorentzian Lichnerowicz Conjecture for real analytic Lorentzian manifolds with finite fundamental group.
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Additional Information
  • Karin Melnick
  • Affiliation: Department of Mathematics, 4176 Campus Drive, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 819221
  • Email: karin@math.umd.edu
  • Vincent Pecastaing
  • Affiliation: Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université Côte d’Azur, Parc Valrose, 06108 Nice, Cedex 2, France
  • MR Author ID: 1154224
  • ORCID: 0000-0003-2118-5238
  • Email: vincent.pecastaing@unice.fr
  • Received by editor(s): February 13, 2020
  • Published electronically: July 12, 2021
  • Additional Notes: This project was initiated during an extended visit by the second author to the University of Maryland supported by GEAR Network grant DMS-1107452, 1107263, 1107367 from the NSF. The first author gratefully acknowledges support from NSF grant DMS-1255462 and from the Max-Planck-Institut für Mathematik in Bonn, where she was a Visiting Scientist during much of the research for this paper. The second author was also partially supported by FNR grants INTER/ANR/15/11211745 and OPEN/16/11405402 while a Postdoctoral Researcher at the University of Luxembourg during much of the research and the writing of this paper.
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 35 (2022), 81-122
  • MSC (2020): Primary 53C50, 57S20
  • DOI: https://doi.org/10.1090/jams/976
  • MathSciNet review: 4322390