Geodesic
On the Hausdorff Dimension of CAT(κ) Surfaces
Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1.

Voir la notice de l'article provenant de la source The Polish Digital Mathematics Library

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.
Mots-clés : metric geometry, Hausdorff dimension, CAT(k) surface, topological entropy 
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Constantine, David; Lafont, Jean-François. On the Hausdorff Dimension of CAT(κ) Surfaces. Analysis and Geometry in Metric Spaces, Tome 4 (2016) no. 1. http://geodesic.mathdoc.fr/item/AGMS_2016_4_1_a2/