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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sub-Riemannian balls in CR Sasakian manifolds
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by Fabrice Baudoin and Michel Bonnefont PDF
Proc. Amer. Math. Soc. 141 (2013), 3919-3924 Request permission

Abstract:

By using sub-Riemannian Li-Yau type heat kernel estimates we prove global estimates for the sub-Riemannian distance of CR Sasakian manifolds with nonnegative horizontal Webster-Tanaka Ricci curvature. In particular, in this setting, large sub-Riemannian balls are comparable to Riemannian balls.
References
  • F. Baudoin, M. Bonnefont and N. Garofalo, A sub-Riemannian curvature-dimension inequality, volume doubling property and the Poincaré inequality, arXiv:1007.1600, submitted (2010).
  • F. Baudoin and N. Garofalo, Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, arXiv:1101.3590, submitted (2009).
  • Sorin Dragomir and Giuseppe Tomassini, Differential geometry and analysis on CR manifolds, Progress in Mathematics, vol. 246, Birkhäuser Boston, Inc., Boston, MA, 2006. MR 2214654, DOI 10.1007/0-8176-4483-0
  • C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 590–606. MR 730094
  • Misha Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, vol. 152, Birkhäuser Boston, Inc., Boston, MA, 1999. Based on the 1981 French original [ MR0682063 (85e:53051)]; With appendices by M. Katz, P. Pansu and S. Semmes; Translated from the French by Sean Michael Bates. MR 1699320
  • David Jerison and Antonio Sánchez-Calle, Subelliptic, second order differential operators, Complex analysis, III (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1277, Springer, Berlin, 1987, pp. 46–77. MR 922334, DOI 10.1007/BFb0078245
  • Alexander Nagel, Elias M. Stein, and Stephen Wainger, Balls and metrics defined by vector fields. I. Basic properties, Acta Math. 155 (1985), no. 1-2, 103–147. MR 793239, DOI 10.1007/BF02392539
  • Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
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Additional Information
  • Fabrice Baudoin
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • MR Author ID: 690937
  • ORCID: 0000-0001-5645-1060
  • Email: fbaudoin@math.purdue.edu
  • Michel Bonnefont
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Received by editor(s): January 23, 2012
  • Published electronically: July 24, 2013
  • Additional Notes: The first author was supported in part by NSF Grant DMS 0907326
  • Communicated by: Lei Ni
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 3919-3924
  • MSC (2010): Primary 32V20, 58J35
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11783-1
  • MathSciNet review: 3091781