Margulis Multiverse: Infinitesimal Rigidity, Pressure Form and Convexity
arXiv:1907.12348 · doi:10.1090/tran/8864
Abstract
In this article we construct the pressure form on the moduli space of higher dimensional Margulis spacetimes without cusps and study its properties. We show that the Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectrums. We use it to show that the restrictions of the pressure form give Riemannian metrics on the constant entropy sections of the quotient moduli space. We also show that constant entropy sections of the moduli space with fixed linear part bound convex domains.
35 pages, no figures
References in corpus (14)
- Anosov representations: Domains of discontinuity and applications
- Anosov representations and dominated splittings
- Dynamics on flag manifolds: domains of proper discontinuity and cocompactness
- Topological Invariants of Anosov Representations
- Morse actions of discrete groups on symmetric space
- Hyperconvex representations and exponential growth
- Flows and joins of metric spaces
- The Auslander conjecture for dimension less than 7
- Proper affine actions on semisimple Lie algebras
- Proper affine actions for right-angled Coxeter groups
- Affine Anosov representations and proper actions
- Proper affine deformation spaces of two-generator Fuchsian groups
- Proper affine actions in non-swinging representations
- The Pressure Metric on the Margulis Multiverse