Convex decompositions of real projective surfaces. I: \(\pi\)-annuli and convexity (Q1336258)

The author considers an orientable compact projective surface \(\Sigma\) with convex boundary and negative Euler characteristic. He supposes that \(\Sigma\) is not convex. He proves in his main result that there is a \(\pi\)-annulus \(\Lambda\) with a projective map \(\Phi: \Lambda\to \Sigma\).