Entropy degeneration of convex projective surfaces
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- by Xin Nie
- Conform. Geom. Dyn. 19 (2015), 318-322
- DOI: https://doi.org/10.1090/ecgd/286
- Published electronically: December 7, 2015
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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.References
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Bibliographic 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
- © Copyright 2015 American Mathematical Society
- Journal: Conform. Geom. Dyn. 19 (2015), 318-322
- MSC (2010): Primary 51H20, 53C23, 37A35
- DOI: https://doi.org/10.1090/ecgd/286
- MathSciNet review: 3432325