Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two

Xueping Li

Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two

Differential Geometry 2013-01-08 v1 Metric Geometry

Authors: Xueping Li

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.

Keywords

Alexandrov spaces nonnegative curvature soul codimension two Sharafutdinov retraction submetry structural results

Cite

@article{arxiv.1301.1238,
  title  = {Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two},
  author = {Xueping Li},
  journal= {arXiv preprint arXiv:1301.1238},
  year   = {2013}
}

Comments

30 pages

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