Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Abstract

In this note we discuss estimates for the curvature of 4-dimensional gradient Ricci soliton singularity models by applying Perelman's point selection, a fundamental result of Cheeger and Naber, and topological lemmas.

Revised version, as appeared in Advances in Mathematics 372 (2020), article number 107303. We would like to thank the referee for their suggestions

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• On curvature estimates for four-dimensional gradient Ricci solitons
• Four-dimensional gradient Ricci solitons with (half) nonnegative isotropic curvature
• Asymptotically cylindrical steady Kähler-Ricci solitons