# On the Hausdorff Dimension of CAT(κ) Surfaces

David Constantine; Jean-François Lafont

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 266-277, electronic only
- ISSN: 2299-3274

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topDavid 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 -

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