Trace theory for gauge-covariant Sobolev spaces

TL;DR

This paper characterizes the traces of gauge-covariant Sobolev spaces on Riemannian vector bundles as gauge-covariant fractional Sobolev spaces under bounded curvature conditions, extending known magnetic Sobolev space results.

Contribution

It provides a new characterization of gauge-covariant Sobolev space traces in terms of fractional Sobolev spaces, with curvature-dependent constants.

Findings

Trace and extension constants depend only on curvature

Recovers known results for magnetic Sobolev spaces in abelian case

Characterizes gauge-covariant Sobolev space traces under bounded curvature

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.