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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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
Mathematical Subject Classification 2000
Primary: 53C23
Secondary: 51H25
References
Publication
Received: 11 August 2011
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