CAT(κ)曲面的Hausdorff维数

Pub Date : 2016-03-01 DOI:10.1515/agms-2016-0010

D. Constantine, J.-F. Lafont

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引用次数: 3

摘要

摘要证明了具有CAT(κ)度量的封闭曲面具有Hausdorff维数= 2，并且证明了小度量球的二维Hausdorff维数存在均匀的上界和下界。我们还讨论了这种均匀性条件与这种表面的测地线流动动力学的一些结果之间的联系。最后，我们给出了在特定CAT(−1)流形上测地线流的拓扑熵刚性的一个简短证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Hausdorff Dimension of CAT(κ) Surfaces

Abstract We prove that a closed surface with a CAT(κ) metric has Hausdorff dimension = 2, and that there are uniform upper and lower bounds on the two-dimensional Hausdorff measure of small metric balls. We also discuss a connection between this uniformity condition and some results on the dynamics of the geodesic flow for such surfaces. Finally,we give a short proof of topological entropy rigidity for geodesic flow on certain CAT(−1) manifolds.

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