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Conformal Geometry and Dynamics

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Entropy degeneration of convex projective surfaces

Author: Xin Nie
Journal: Conform. Geom. Dyn. 19 (2015), 318-322
MSC (2010): Primary 51H20, 53C23, 37A35
Published electronically: December 7, 2015
MathSciNet review: 3432325
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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.

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Additional Information

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

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