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Entropy rigidity for finite volume strictly convex projective manifolds

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Abstract

We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions \(\ge 3\), generalizing the work of [1] to the finite volume setting. The rigidity theorem uses the techniques of Besson, Courtois, and Gallot’s entropy rigidity theorem. It implies uniform lower bounds on the volume of any finite volume strictly convex projective manifold in dimensions \(\ge 3\).

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Notes

  1. see experimental work and images generated by Marianne DeBrito, Andrew Nguyen, and Marisa O’Gara as a part of the LoGM program at the University of Michigan here: https://gitlab.eecs.umich.edu/logm/wi20/entropy-project-outputs

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Acknowledgements

We would like to thank Dick Canary and Ralf Spatzier for helpful conversations about this project. D.C. would like to thank the University of Michigan for hosting him on a short visit during which a portion of this work was completed.

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Authors and Affiliations

  1. George Mason University, Fairfax, VA, USA

    Harrison Bray

  2. Wesleyan University, Middletown, CT, USA

    David Constantine

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  1. Harrison Bray
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  2. David Constantine
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Correspondence to David Constantine.

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Bray, H., Constantine, D. Entropy rigidity for finite volume strictly convex projective manifolds. Geom Dedicata 214, 543–557 (2021). https://doi.org/10.1007/s10711-021-00627-w

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