Remote Access Conformal Geometry and Dynamics
Green Open Access

Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

Entropy degeneration of convex projective surfaces


Author: Xin Nie
Journal: Conform. Geom. Dyn. 19 (2015), 318-322
MSC (2010): Primary 51H20, 53C23, 37A35
DOI: https://doi.org/10.1090/ecgd/286
Published electronically: December 7, 2015
MathSciNet review: 3432325
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the fact, due to Benoist and Hulin, that the Hilbert metric and the Blaschke metric are comparable.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 51H20, 53C23, 37A35

Retrieve articles in all journals with MSC (2010): 51H20, 53C23, 37A35


Additional Information

Xin Nie
Affiliation: School of Mathematics, KIAS, 85 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea.
MR Author ID: 1040171
Email: nie.hsin@gmail.com

Received by editor(s): May 28, 2015
Received by editor(s) in revised form: November 11, 2015
Published electronically: December 7, 2015
Additional Notes: The research leading to these results has received funding from the European Research Council under the European Community’s seventh Framework Programme (FP7/2007-2013)/ERC grant agreement no. FP7-246918
Article copyright: © Copyright 2015 American Mathematical Society