Abstract
LetX be a Riemannian symmetric space of noncompact type and rank≧2 and let Γ be a non-uniform, irreducible lattice. On the locally symmetric quotientV=Γ/X we construct an exhaustion functionh:V→[0,∞) whose sublevel sets {h≦s} are compact submanifolds ofV with corners. The top dimensional boundary faces of {h≦s} are parts of certain horospheres that join together at the corners. It can be shown that actually {h≦s} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.
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Oblatum 2-VIII-1993 & 19-XII-1994
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Leuzinger, E. An exhaustion of locally symmetric spaces by compact submanifolds with corners. Invent Math 121, 389–410 (1995). https://doi.org/10.1007/BF01884305
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DOI: https://doi.org/10.1007/BF01884305