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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Generalized Kähler-Ricci flow on toric Fano varieties
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by Vestislav Apostolov, Jeffrey Streets and Yury Ustinovskiy PDF
Trans. Amer. Math. Soc. 375 (2022), 4369-4409 Request permission

Abstract:

We study the generalized Kähler-Ricci flow with initial data of symplectic type, and show that this condition is preserved. In the case of a Fano background with toric symmetry, we establish global existence of the normalized flow. We derive an extension of Perelman’s entropy functional to this setting, which yields convergence of nonsingular solutions at infinity. Furthermore, we derive an extension of Mabuchi’s $K$-energy to this setting, which yields weak convergence of the flow.
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Additional Information
  • Vestislav Apostolov
  • Affiliation: Départment de matheématiques, Université du Québec à Montréal, Case postale 8888, succursale centre-ville, Mongtréal (Québec) H3C 3P8, Canada
  • MR Author ID: 366272
  • ORCID: 0000-0002-6445-2773
  • Email: apostolov.vestislav@uqam.ca
  • Jeffrey Streets
  • Affiliation: Rowland Hall, University of California, Irvine, California 92617
  • MR Author ID: 828981
  • Email: jstreets@uci.edu
  • Yury Ustinovskiy
  • Affiliation: Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012-1185
  • MR Author ID: 887998
  • ORCID: 0000-0002-2510-4098
  • Email: yuraust@gmail.com
  • Received by editor(s): April 14, 2021
  • Received by editor(s) in revised form: August 6, 2021, August 19, 2021, and November 8, 2021
  • Published electronically: March 16, 2022
  • Additional Notes: The second author was supported by the NSF via DMS-1454854. The first author was supported in part by an NSERC Discovery Grant
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 4369-4409
  • MSC (2020): Primary 53E30, 53D18
  • DOI: https://doi.org/10.1090/tran/8619
  • MathSciNet review: 4419062