Vol. 163, No. 1, 1994

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On complete Riemannian manifolds with collapsed ends

Zhongmin Shen

Vol. 163 (1994), No. 1, 175–182
Abstract

We show that if a complete open manifold with bounded curvature and sufficiently small ends, then each end is an infranilend. Conversely, an open manifold with finitely many infranilends admits a complete metric with bounded curvature and arbitrarily small ends.

Mathematical Subject Classification 2000
Primary: 53C20
Secondary: 53C23
Milestones
Received: 23 April 1992
Published: 1 March 1994
Authors
Zhongmin Shen