The Margulis Lemma and the Thick and Thin Decomposition for Convex Real Projective Surfaces

@inproceedings{Choi1996TheML,
  title={The Margulis Lemma and the Thick and Thin Decomposition for Convex Real Projective Surfaces},
  author={Suhyoung Choi},
  year={1996}
}
Convex real projective surfaces are quotients of simply convex domains in the real projective planeRP2under the properly discontinuous and free action of a projective automorphism group. Such surfaces carry Hilbert metrics defined by logarithms of cross ratios. We prove an analogous proposition to the Margulis lemma in hyperbolic geometry holding for such a surfaceΣwith a Hilbert metric. This allows us to decomposeΣinto thick and thin components. We show a compactness result that given a… CONTINUE READING