4 papers
On the singularity formation of gauge fields coupled to Ricci flow
Andoni 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 th…
Regularity of conformal structures on closed 3-manifolds
Rodrigo Avalos, Albachiara Cogo, Andoni Royo Abrego
It is well known in Riemannian geometry that the metric components have the best regularity in harmonic coordinates. These can be used to characterize the most regular element in t…
Conformal Green functions and Yamabe metrics of Sobolev regularity
Rodrigo Avalos, Albachiara Cogo, Andoni Royo Abrego
We provide a full resolution of the Yamabe problem on closed 3-manifolds for Riemannian metrics of Sobolev class with . This requires developing an elliptic theory…
Ancient solutions of Ricci flow with Type I curvature growth
Stephen 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 natu…