Trace theory for gauge-covariant Sobolev spaces

Abstract

The traces of gauge-covariant Sobolev spaces on a Riemannian vector bundle endowed with a metric 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.