An exhaustion of locally symmetric spaces by compact submanifolds with corners

LetX be a Riemannian symmetric space of noncompact type and rank2 and let be a non-uniform, irreducible lattice. On the locally symmetric quotientV=/X we construct an exhaustion functionh:V0,) whose sublevel sets {hs} are compact submanifolds ofV with corners. The top dimensional boundary faces of {hs} are parts of certain horospheres that join together at the corners. It can be shown that actually {hs} is a submanifold with corners isomorphic to the Borel-Serre compactification ofV.Oblatum 2-VIII-1993 & 19-XII-1994