https://neckpinch.com/authors/patrick-donovan/New arXiv papers by Patrick Donovan, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2503.15033/arxiv:2503.15033Wed, 19 Mar 2025 00:00:00 GMTPatrick Donovan — Simply-connected four-dimensional gradient Ricci solitons that are invariant under a compact cohomogeneity one group action have been studied extensively. However, the special case where the group is SU(2) (the smallest possible example) has received comparatively little attention. The purpose of this article is to give a comprehensive study of simply-connected SU(2)-invariant expanding and shrinking cohomogeneity one gradient Ricci solitons. The first result is the construction of new 3-parameter families of complete SU(2)-invariant asymptotically conical expanding gradient Ricci solitons. New shrinking Kähler U(2)-invariant gradient Ricci solitons in dimension 4 with orbifold singularities are also constructed, leading to a classification of such metrics when the base space of the orbifold is a simply-connected smooth manifold. Finally, we highlight numerical evidence that all the compact cohomogeneity one shrinking gradient Ricci solitons are known.Ricci solitonsSingularities4-manifoldsKähler geometryHomogeneous spacesBoundaries & non-compactNumerics & visualization