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Convex decompositions of real projective surfaces. I. $\pi$-annuli and convexity
A real protective surface is a surface with a flat real projective structure.A π-annulus is an easy-to-construct real projective annulus with geodesic boundary.Let Σ be an orientable compact real projective surface with convex boundary and negative Euler characteristic.We prove that there is a π-annulus with a projective map to Σ …