Complete noncompact Alexandrov spaces of nonnegative curvature
Let \(X\) be a complete noncompact length metric space, which outside a compact set is locally an \(n\)-dimensional Alexandrov space of nonnegative curvature. The main theorem of this paper is that \(X\) has unbounded \(n\)- dimensional Hausdorff volume. It might have been helpful to point out that the proof depends on a slight generalization of the Burago-Gromov- Perelman-Toponogov comparison theorem, so as to omit a compact set. The end structure of nonnegatively curved Alexandrov spaces is also discussed.
scientific article; zbMATH DE number 446327