Pohozaev identities and bubbling obstruction for Yang-Mills fields in conformal dimension

TL;DR

This paper investigates bubbling phenomena in Yang-Mills fields on four-manifolds, deriving Pohozaev identities that reveal obstructions to bubbling and applying these results to specific geometric cases.

Contribution

It extends previous bubbling obstruction results by incorporating the Weyl tensor, providing new insights into Yang-Mills fields in conformal geometry.

Findings

Derived Pohozaev-type identities relating weak limits and bubbles involving the Weyl tensor.

Extended bubbling obstruction results beyond locally conformally flat cases.

Ruled out certain bubbling configurations on CP2.

Abstract

We study bubbling for sequences of Yang-Mills connections on closed four-manifolds and we derive a compatibility of Pohozaev type between the weak limit connection and the bubble formed at a concentration point, involving the Weyl tensor of the background metric. This yields obstruCtions to bubbling extending earlier results of Yin beyond the locally conformally flat case. As an application, we rule out certain bubbling configurations on CP2.