Hölder分布次黎曼距离的一个下界
A lower bound on the subriemannian distance for Hölder distributions
摘要：
虽然次黎曼几何通常处理光滑的水平分布，但部分双曲动力系统提供了许多由非光滑（即霍德连续）分布定义的次黎曼几何的例子。这些分布对于父动力系统的行为具有重要意义。因此，对霍尔德次黎曼几何的研究可以为动力学和次黎曼几何提供新的见解。在本文中，我们在这个方向上迈出了一小步：我们证明了一个Hölder型下界的次黎曼距离的Hölder连续无处可积余维1分布。该界推广了光滑情形下的平方根界。
英文摘要：
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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