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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A lower bound on the subriemannian distance for Hölder distributions


Author: Slobodan N. Simic
Journal: Proc. Amer. Math. Soc. 138 (2010), 3293-3299
MSC (2010): Primary 51F99, 53B99
Published electronically: April 16, 2010
MathSciNet review: 2653959
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Abstract: Whereas subriemannian geometry usually deals with smooth horizontal distributions, partially hyperbolic dynamical systems provide many examples of subriemannian geometries defined by non-smooth (namely, Hölder continuous) distributions. These distributions are of great significance for the behavior of the parent dynamical system. The study of Hölder subriemannian geometries could therefore offer new insights into both dynamics and subriemannian geometry. In this paper we make a small step in that direction: we prove a Hölder-type lower bound on the subriemannian distance for Hölder continuous nowhere integrable codimension one distributions. This bound generalizes the well-known square root bound valid in the smooth case.


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Additional Information

Slobodan N. Simic
Affiliation: Department of Mathematics, San José State University, San José, California 95192-0103
Email: simic@math.sjsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-10-10350-5
PII: S 0002-9939(10)10350-5
Keywords: Distribution, H\"older continuity, subriemannian distance
Received by editor(s): June 29, 2009
Received by editor(s) in revised form: December 18, 2009, and December 23, 2009
Published electronically: April 16, 2010
Communicated by: Bryna Kra
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.