The Dirac Spectrum   Nicolas Ginoux

第一章   Basics of spin geometry

  1. Spin group and spin structure      [Spin(3)   Spin(4)]
  2. Spin bundle and Clifford multiplication
  3. The Dirac operator
  4. Spinors on hypersurfaces and coverings
  5. Elliptic boundary conditions for the Dirac operator

第二章   Explicit comutations of spectra

  1. Spectrum of some non-negatively curved spaceforms
  2. Spectrum of some other homogeneous spaces
  3. Small eigenvalues of some symmetric spaces

第三章   Lower eigenvalue estimates on closed manifolds

  1. Friedrich inequality
  2. Improving Friedrich inequality in presence of a parallel form
  3. Improving Friedrich inequality in a conformal way
  4. Improvinh Friedrich inequality with the energy-momentum tensor
  5. Improving Freidrich inequality with other curvature components
  6. Improvinh Friedrich inequality on surfaces of positive genus
  7. Improving Friedrich inequality on bounding manifolds

第四章   Lower eigenvalue estimate on compact manifolds with boundary

  1.  

第五章   Upper eigenvalue bounds on closed manifolds

第六章   Prescription of eigenvalues on closed manifolds

第七章   The Dirac spectrum on non-compact manifolds

  1. Essential and point spectrum
  2. Explicit computation of spectra
  3. Lower bounds on the spectrum
  4. Absence of a spectral component

第八章   Other topics related with the Dirac spectrum

附錄      The twistor and Killing spinor equations