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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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Patterson–Sullivan theory for Anosov subgroups
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by Subhadip Dey and Michael Kapovich PDF
Trans. Amer. Math. Soc. 375 (2022), 8687-8737 Request permission

Abstract:

We extend several notions and results from the classical Patterson–Sullivan theory to the setting of Anosov subgroups of higher rank semisimple Lie groups, working primarily with invariant Finsler metrics on associated symmetric spaces. In particular, we prove the equality between the Hausdorff dimensions of flag limit sets, computed with respect to a suitable Gromov (pre-)metric on the flag manifold, and the Finsler critical exponents of Anosov subgroups.
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Additional Information
  • Subhadip Dey
  • Affiliation: Department of Mathematics, Yale University, 10 Hillhouse Ave, New Haven, Connecticut 06511
  • MR Author ID: 1289428
  • Email: subhadip.dey@yale.edu
  • Michael Kapovich
  • Affiliation: Department of Mathematics, University of California, Davis, One Shields Ave, Davis, California 95616
  • MR Author ID: 98110
  • ORCID: 0000-0001-5475-8755
  • Email: kapovich@math.ucdavis.edu
  • Received by editor(s): July 6, 2020
  • Received by editor(s) in revised form: December 5, 2021, and March 20, 2022
  • Published electronically: September 23, 2022
  • Additional Notes: The second author was partly supported by the NSF grant DMS-16-04241
  • © Copyright 2022 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8687-8737
  • MSC (2020): Primary 20F65, 22E40, 53C35
  • DOI: https://doi.org/10.1090/tran/8713