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.
Author(s): Nicolas Ginoux (auth.)
Series: Lecture Notes in Mathematics 1976
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2009
Language: English
Pages: 156
Tags: Partial Differential Equations; Differential Geometry; Global Analysis and Analysis on Manifolds
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
