3 papers
math.DG2025
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…
math.AP2025
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…
math.DG2024
Sobolev regularity of compactified 3-manifolds and the ADM Center of Mass
Rodrigo Avalos
In this paper, we address the existence of preferred asymptotic coordinates on asymptotically Euclidean (AE) manifolds such that admits an asymptotically Schwarzschil…