Entropy rigidity for finite volume strictly convex projective manifolds

TL;DR

This paper proves entropy rigidity for finite volume strictly convex projective manifolds in dimensions three and higher, extending previous results to the finite volume case and establishing volume lower bounds.

Contribution

It generalizes entropy rigidity results to finite volume manifolds, using techniques from Besson, Courtois, and Gallot, and provides volume lower bounds in higher dimensions.

Findings

Entropy rigidity holds for finite volume strictly convex projective manifolds in dimensions ≥3.

Establishes uniform lower bounds on the volume of such manifolds.

Extends previous rigidity results to the finite volume setting.

Abstract

We prove entropy rigidity for finite volume strictly convex projective manifolds in dimensions $\geq 3$, generalizing the work of arXiv:1708.03983 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 $\geq 3$.