The Dirac spectrum

Nicolas Ginoux (auth.)3642015697, 9783642015694, 3642015700, 9783642015700

This volume surveys the spectral properties of the spin Dirac operator. After a brief introduction to spin geometry, we present the main known estimates for Dirac eigenvalues on compact manifolds with or without boundaries. We give examples where the spectrum can be made explicit and present a chapter dealing with the non-compact setting. The methods mostly involve elementary analytical techniques and are therefore accessible for Master students entering the subject. A complete and updated list of references is also included.

Table of contents :
Front Matter….Pages 1-11
Basics of spin geometry….Pages 1-27
Explicit computations of spectra….Pages 29-39
Lower eigenvalue estimates on closed manifolds….Pages 41-68
Lower eigenvalue estimates on compact manifolds with boundary….Pages 69-75
Upper eigenvalue bounds on closed manifolds….Pages 77-92
Prescription of eigenvalues on closed manifolds….Pages 93-101
The Dirac spectrum on non-compact manifolds….Pages 103-111
Other topics related with the Dirac spectrum….Pages 113-129
Back Matter….Pages 1-32