The Dirac spectrum

by Nicolas Ginoux

Lecture Notes in Mathematics 1976 (2009), Springer

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Summary: This book 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 boundary. We give examples where the spectrum can be made explicit and 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. We include a complete and updated list of references.

Nicolas Ginoux, 10.03.2011