Compactness theorems for 4-dimensional gradient Ricci solitons

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)361-384
Number of pages24
JournalPacific Journal of Mathematics
Volume303
Issue number1
DOIs
StatePublished - Jan 1 2019

Keywords

  • Compactness
  • Ricci soliton
  • dimension four

Fingerprint Dive into the research topics of 'Compactness theorems for 4-dimensional gradient Ricci solitons'. Together they form a unique fingerprint.

  • Cite this