The degeneration of convex ℝℙ2structures on surfaces

Abstract

Let M be a compact surface of negative Euler characteristic and let C(M) be the deformation space of convex real projective structures on M. For every choice of pants decomposition for M, there is a well known parameterization of C(M) known as the Goldman parameterization. In this paper, we study how some geometric properties of the real projective structure on M degenerates as we deform it so that the internal parameters of the Goldman parameterization leave every compact set while the boundary invariants remain bounded away from zero and infinity.