Trace theory for gauge-covariant Sobolev spaces
arXiv:2501.17254 · doi:10.1016/j.jmaa.2025.129697
Abstract
The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle for some connection are characterised as some gauge-covariant fractional Sobolev spaces when the curvature of the connection is bounded. The constants in the trace and extension theorems only depend on this curvature. When the connection is abelian, one recovers known results for magnetic Sobolev spaces.
arXiv comment31 pages