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American Mathematical Society, Proceedings of the American Mathematical Society, 09(138), p. 3293-3293

DOI: 10.1090/s0002-9939-10-10350-5

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A lower bound on the subriemannian distance for Ḧolder distributions

Journal article published in 2007 by Slobodan N. Simić
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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, H\"older continuous) distributions. These distributions are of great significance for the behavior of the parent dynamical system. The study of H\"older 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 H\"older-type lower bound on the subriemannian distance for H\"older continuous nowhere integrable codimension one distributions. This bound generalizes the well-known square root bound valid in the smooth case. Comment: 8 pages, 2 figures. Few improvements and minor corrections. To appear in the Proceedings of the AMS