Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two

Abstract

In this paper, we study a complete noncompact nonnegatively curved Alexandrov space $A$ with a soul $S$ of codimension two. We establish some structural results under additional regularity assumptions. As an application, we conclude that in this case Sharafutdinov retraction, $\pi :A\to S$, is a submetry.

30 pages

References in corpus (1)

• An optimal extension of Perelman's comparison theorem for quadrangles and its applications