The Birman-Krein formula for differential forms and electromagnetic scattering

We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of low regularity we prove a Birman-Krein formula on the space of co-closed differential forms. In the case of dimension thre...

Full description

Saved in:
Bibliographic Details
Main Authors Strohmaier, Alexander, Waters, Alden
Format Journal Article
LanguageEnglish
Published 28.04.2021
Subjects
Mathematics - Analysis of PDEs
Mathematics - Mathematical Physics
Mathematics - Spectral Theory
Physics - Mathematical Physics
Online AccessGet full text

Cover

More Information
Summary:We consider scattering theory of the Laplace Beltrami operator on differential forms on a Riemannian manifold that is Euclidean near infinity. Allowing for compact boundaries of low regularity we prove a Birman-Krein formula on the space of co-closed differential forms. In the case of dimension three this reduces to a Birman-Krein formula in Maxwell scattering.
DOI:10.48550/arxiv.2104.13589