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arXiv · 2610.35257

Bach-flat metrics and global regularity of conformal structures

Rodrigo Avalos·Albachiara Cogo·Andoni Royo Abrego
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Abstract

We study global regularity properties of conformal structures on compact manifolds with applications to conformally invariant variational problems. We find sharp conditions ensuring that a manifold equipped with a Riemannian metric of Sobolev class is conformally diffeomorphic to a smooth one. In particular, we prove that $W^{2,q}$ Bach-flat four-manifolds with $q > 2$ are smooth up to conformal diffeomorphisms. We also solve the Yamabe problem for $W^{2,q}$ metrics with $q > 2$ on three-manifolds under a mild conformal condition.

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Rodrigo Avalos, Albachiara Cogo, Andoni Royo Abrego. 2026-10-26. Bach-flat metrics and global regularity of conformal structures. https://arxiv.org/abs/2610.35257

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