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Abstract
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We prove compactness theorems for noncompact 4-dimensional shrinking and steady
gradient Ricci solitons, respectively, satisfying: (1) every bounded open subset can be
embedded in a closed 4-manifold with vanishing second homology group, and (2) are strongly
-noncollapsed on all scales
with respect to a uniform
.
These solitons are of interest because they are the only ones that can arise as
finite-time singularity models for a Ricci flow on a closed 4-manifold with vanishing
second homology group.
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Keywords
dimension four, Ricci soliton, compactness
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Mathematical Subject Classification 2010
Primary: 53C44
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Milestones
Received: 16 August 2018
Revised: 15 January 2019
Accepted: 4 April 2019
Published: 21 December 2019
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