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Convex decompositions of real projective surfaces. I: \(\pi\)-annuli and convexity. (English) Zbl 0818.53042

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 \(\Phi: \Lambda\to \Sigma\).

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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