Convexes divisibles IV : Structure du bord en dimension 3
成果类型：
Article
署名作者：
Benoist, Y
署名单位：
Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS)
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-005-0478-4
发表日期：
2006
页码：
249-278
关键词：
摘要：
Let Omega be an indecomposable properly convex open subset of the real projective 3-space which is divisible i.e. for which there exists a torsion free discrete group Gamma of projective transformations preserving Omega such that the quotient M := Gamma\Omega is compact. We study the structure of M and of partial derivative Omega, when Omega is not strictly convex: The union of the properly embedded triangles in Omega projects in M onto an union of finitely many disjoint tori and Klein bottles which induces an atoroidal decomposition of M. Every non extremal point of partial derivative Omega is on an edge of a unique properly embedded triangle in Omega and the set of vertices of these triangles is dense in the boundary of Omega (see Figs. 1 to 4). Moreover, we construct examples of such divisible convex open sets Omega.
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