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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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Topology and dynamics of laminations in surfaces of general type
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by Bertrand Deroin and Christophe Dupont PDF
J. Amer. Math. Soc. 29 (2016), 495-535 Request permission

Abstract:

We study Riemann surface laminations in complex algebraic surfaces of general type. We focus on the topology and dynamics of minimal sets of holomorphic foliations and on Levi-flat hypersurfaces. We begin by providing various examples. Then our first result shows that Anosov Levi-flat hypersurfaces do not embed in surfaces of general type. This allows one to classify the possible Thurston’s geometries carried by Levi-flat hypersurfaces in surfaces of general type. Our second result establishes that minimal sets in surfaces of general type have a large Hausdorff dimension as soon as there exists a simply connected leaf. For both results, our methods rely on ergodic theory: we use harmonic measures and Lyapunov exponents.
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Additional Information
  • Bertrand Deroin
  • Affiliation: Ecole Normale Supérieure, DMA, UMR CNRS 8553, 45 rue d’Ulm, 75230 Paris Cedex 05, France
  • MR Author ID: 727583
  • Email: bertrand.deroin@ens.fr
  • Christophe Dupont
  • Affiliation: Université de Rennes 1, IRMAR, UMR CNRS 6625, 35042 Rennes Cedex, France
  • MR Author ID: 718471
  • Email: christophe.dupont@univ-rennes1.fr
  • Received by editor(s): May 11, 2012
  • Received by editor(s) in revised form: July 31, 2013, November 28, 2014, and March 9, 2015
  • Published electronically: June 2, 2015
  • Additional Notes: The research leading to these results has received funding from the European Research Council under the European Community’s seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. FP7-246918, and from the ANR projects Dynacomplexe ANR-07-JCJC-0006 and LAMBDA, ANR-13-BS01-0002.
    The first author was supported by the ANR projects 08-JCJC-0130-01 and 09-BLAN-0116.
    The second author was supported by the ANR project 07-JCJC-0006-01.

  • Dedicated: To the memory of Marco Brunella
  • © Copyright 2015 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 29 (2016), 495-535
  • MSC (2010): Primary 32V30, 37C85; Secondary 37F75, 37C45
  • DOI: https://doi.org/10.1090/jams832
  • MathSciNet review: 3454381