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arXiv · 1503.04420

Entropy degeneration of convex projective surfaces

Xin Nie
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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 theorem, due to Benoist and Hulin, that the Hilbert metric and Blaschke metric are comparable.

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Xin Nie. 2015-03-15. Entropy degeneration of convex projective surfaces. https://doi.org/10.1090/ecgd%2F286

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