A splitting theorem for nonnegatively curved Alexandrov spaces

Wörner, Andreas

doi:10.2140/gt.2012.16.2391

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A splitting theorem for nonnegatively curved Alexandrov spaces

Andreas Wörner

Geometry & Topology 16 (2012) 2391–2426

DOI: 10.2140/gt.2012.16.2391

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

Volume 16, issue 4 (2012)