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On the Hausdorff Dimension of CAT(κ) Surfaces

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Constantine D., Lafont J.-F.

Analysis and Geometry in Metric Spaces

2016

tom 4

nr 1

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.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Constantine D.

1 Lafont J.-F.

1 2016

Wyniki wyszukiwania

On the Hausdorff Dimension of CAT(κ) Surfaces