https://neckpinch.com/authors/andoni-royo-abrego/New arXiv papers by Andoni Royo Abrego, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2609.27644/arxiv:2609.27644Wed, 23 Sep 2026 00:00:00 GMTAndoni Royo Abrego — We study a family of coupled geometric evolution equations describing the deformation of a Riemannian metric and a non-abelian gauge field on closed manifolds, which generalizes the Ricci–Yang–Mills flow. We derive interior curvature estimates, find a preserved integral curvature condition, and discover a scaling invariant monotone functional analogue to Perelman's entropy. In particular, we prove strong dominance of the Riemannian curvature over the gauge curvature at finite-time singularities in all dimensions. We also provide a non-trivial explicit example of a shrinking self-similar solution on a SU(2) bundle over S⁴.Ricci flowSingularitiesPerelman entropy https://neckpinch.com/papers/2211.06253/arxiv:2211.06253Fri, 11 Nov 2022 00:00:00 GMTStephen Lynch, Andoni Royo Abrego — Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natural geometric assumptions. Nonnegatively curved solutions in dimensions 2 and 3, and uniformly PIC solutions in higher dimensions are now well understood. We consider ancient solutions of arbitrary dimension which are complete and have Type I curvature growth. We show that a κ-noncollapsed Type I ancient solution which is noncompact and has nonnegative sectional curvature necessarily splits at least one Euclidean factor. It follows that a κ-noncollapsed Type I ancient solution which is weakly PIC2 is a locally symmetric space.Ricci flowAncient solutionsSingularities(Non)collapsingSphere theoremsBoundaries & non-compact