On the Hausdorff Dimension of CAT(κ) Surfaces

• Autorzy: David Constantine , Jean-François Lafont
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

metric geometry; Hausdorff dimension; CAT(k) surface; topological entropy

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2015-03-02

zaakceptowano

2016-07-04

online

2016-09-20

Twórcy

autor

David Constantine

• Department of Mathematics, Ohio State University, Columbus, Ohio 43210

autor

Jean-François Lafont

• Wesleyan University, Mathematics and Computer Science Department, Middletown, CT 06459

Identyfikatory

DOI

10.1515/agms-2016-0010