Analysis and Geometry of Boundary-Manifolds of Bounded Geometry
  In this paper, we investigate analytical and geometric properties of certain non-compact boundary-manifolds, namely manifolds of bounded geometry. One result are strong Bochner type vanishing results for the L^2-cohomology of these manifolds: if e.g. a manifold admits a metric of bounded geometry which outside a compact set has nonnegative Ricci curvature and nonnegative mean curvature (of the boundary) then its first relative L^2-cohomology vanishes (this in particular answers a question of Roe).   We prove the Hodge-de Rham-theorem for L^2-cohomology of oriented boundary-manifolds of bounded geometry.   The technical basis is the study of (uniformly elliptic) boundary value problems on these manifolds, applied to the Laplacian. 
Thomas Schick (Uni M\"unster, Germany; and Penn State University)