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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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A variational approach to the Yau–Tian–Donaldson conjecture
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by Robert J. Berman, Sébastien Boucksom and Mattias Jonsson HTML | PDF
J. Amer. Math. Soc. 34 (2021), 605-652 Request permission

Abstract:

We give a variational proof of a version of the Yau–Tian–Donaldson conjecture for twisted Kähler–Einstein currents, and use this to express the greatest (twisted) Ricci lower bound in terms of a purely algebro-geometric stability threshold. Our approach does not involve a continuity method or the Cheeger–Colding–Tian theory, and uses instead pluripotential theory and valuations. Along the way, we study the relationship between geodesic rays and non-Archimedean metrics.
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Additional Information
  • Robert J. Berman
  • Affiliation: Mathematical Sciences, Chalmers University of Technology; and University of Gothenburg, SE-412 96 Göteborg, Sweden
  • MR Author ID: 743613
  • Email: robertb@chalmers.se
  • Sébastien Boucksom
  • Affiliation: CNRS-CMLS, École Polytechnique, F-91128 Palaiseau Cedex, France
  • MR Author ID: 688226
  • Email: sebastien.boucksom@polytechnique.edu
  • Mattias Jonsson
  • Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
  • MR Author ID: 631360
  • Email: mattiasj@umich.edu
  • Received by editor(s): January 24, 2019
  • Received by editor(s) in revised form: June 2, 2020
  • Published electronically: April 1, 2021
  • Additional Notes: The first author was partially supported by the Swedish Research Council, the European Research Council, the Knut and Alice Wallenberg foundation, and the Göran Gustafsson foundation.
    The second author was partially supported by the ANR projects GRACK, MACK and POSITIVE.
    The third author was partially supported by NSF grants DMS-1600011 and DMS-1900025, the Knut and Alice Wallenberg foundation, and the United States—Israel Binational Science Foundation.
  • © Copyright 2021 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 34 (2021), 605-652
  • MSC (2020): Primary 32Q20, 32Q26
  • DOI: https://doi.org/10.1090/jams/964
  • MathSciNet review: 4334189