#### Volume 16, issue 4 (2012)

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A splitting theorem for nonnegatively curved Alexandrov spaces

### Andreas Wörner

Geometry & Topology 16 (2012) 2391–2426
##### Abstract

We study Alexandrov spaces of nonnegative curvature whose boundaries consist of several strata of codimension 1. If the space is compact and the common intersection of all boundary strata is empty, then the space is a metric product. In particular, this is fulfilled if the compact space has dimension $n$ and contains more than $n+1$ boundary strata. The splitting factors are in general non-flat.

##### Keywords
Alexandrov space, nonnegative curvature, boundary strata, metric splitting
Primary: 53C23
Secondary: 51H25
##### Publication
Revised: 18 August 2012
Accepted: 24 December 2011
Published: 4 February 2013
Proposed: Dmitri Burago
Seconded: Tobias H. Colding, Leonid Polterovich
##### Authors
 Andreas Wörner Charlottenstraße 29 72070 Tübingen Germany