Vol. 303, No. 1, 2019

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Compactness theorems for 4-dimensional gradient Ricci solitons

Yongjia Zhang

Vol. 303 (2019), No. 1, 361–384

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 κ-noncollapsed on all scales with respect to a uniform κ. 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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dimension four, Ricci soliton, compactness
Mathematical Subject Classification 2010
Primary: 53C44
Received: 16 August 2018
Revised: 15 January 2019
Accepted: 4 April 2019
Published: 21 December 2019
Yongjia Zhang
Department of Mathematics
University of Minnesota
Twin Cities, MN 55414
United States