On the Hausdorff Dimension of CAT(κ) Surfaces

David Constantine, and Jean-François Lafont. "On the Hausdorff Dimension of CAT(κ) Surfaces." Analysis and Geometry in Metric Spaces 4.1 (2016): 266-277, electronic only. <http://eudml.org/doc/286779>.

@article{DavidConstantine2016,
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.},
author = {David Constantine, Jean-François Lafont},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {metric geometry; Hausdorff dimension; CAT(k) surface; topological entropy; surface},
language = {eng},
number = {1},
pages = {266-277, electronic only},
title = {On the Hausdorff Dimension of CAT(κ) Surfaces},
url = {http://eudml.org/doc/286779},
volume = {4},
year = {2016},
}

TY - JOUR
AU - David Constantine
AU - Jean-François Lafont
TI - On the Hausdorff Dimension of CAT(κ) Surfaces
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 266
EP - 277, electronic only
AB - 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.
LA - eng
KW - metric geometry; Hausdorff dimension; CAT(k) surface; topological entropy; surface
UR - http://eudml.org/doc/286779
ER -