The Dirac Spectrum
Ginoux, Nicolas.
The Dirac Spectrum [electronic resource] / by Nicolas Ginoux. - XV, 156 p. online resource. - Lecture Notes in Mathematics, 1976 0075-8434 ; . - Lecture Notes in Mathematics, 1976 .
Basics of spin geometry -- Explicit computations of spectra -- Lower eigenvalue estimates on closed manifolds -- Lower eigenvalue estimates on compact manifolds with boundary -- Upper eigenvalue bounds on closed manifolds -- Prescription of eigenvalues on closed manifolds -- The Dirac spectrum on non-compact manifolds -- Other topics related with the Dirac spectrum.
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.
9783642015700
10.1007/978-3-642-01570-0 doi
Global analysis.
Global differential geometry.
Differential equations, partial.
Global Analysis and Analysis on Manifolds.
Differential Geometry.
Partial Differential Equations.
QA614-614.97
514.74
The Dirac Spectrum [electronic resource] / by Nicolas Ginoux. - XV, 156 p. online resource. - Lecture Notes in Mathematics, 1976 0075-8434 ; . - Lecture Notes in Mathematics, 1976 .
Basics of spin geometry -- Explicit computations of spectra -- Lower eigenvalue estimates on closed manifolds -- Lower eigenvalue estimates on compact manifolds with boundary -- Upper eigenvalue bounds on closed manifolds -- Prescription of eigenvalues on closed manifolds -- The Dirac spectrum on non-compact manifolds -- Other topics related with the Dirac spectrum.
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.
9783642015700
10.1007/978-3-642-01570-0 doi
Global analysis.
Global differential geometry.
Differential equations, partial.
Global Analysis and Analysis on Manifolds.
Differential Geometry.
Partial Differential Equations.
QA614-614.97
514.74