Eigenvalue bounds for the Dirac operator

DOI10.2140/pjm.1986.125.117zbMath0605.58044OpenAlexW2038707002MaRDI QIDQ1083746

John Lott

Publication date: 1986

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1986.125.117

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items

Eigenvalues of the Dirac operator on compact spin manifolds under Ricci flow ⋮ A Yamabe type problem on compact spin manifolds ⋮ Spectral bounds for Dirac operators on open manifolds ⋮ The Cauchy problems for Einstein metrics and parallel spinors ⋮ An eigenvalue comparison theorem for the Dirac operator on surfaces ⋮ Generic metrics and the mass endomorphism on spin three-manifolds ⋮ Conformal minoration of the spectrum of the Hodge-de Rham Laplacian ⋮ A variational analysis of the spinorial Yamabe equation on product manifolds ⋮ A spinorial quasilocal mass ⋮ A spin-conformal lower bound of the first positive Dirac eigenvalue ⋮ An estimate on the nodal set of eigenspinors on closed surfaces ⋮ Lower bounds for eigenvalues of the Dirac operator on \(n\)-spheres with \(SO(n)\)-symmetry ⋮ A spinorial analogue of Aubin's inequality ⋮ Some remarks on the Hijazi inequality and generalizations of the Killing equation for spinors ⋮ The first conformal Dirac eigenvalue on 2-dimensional tori ⋮ A spinorial analogue of the Brezis-Nirenberg theorem involving the critical Sobolev exponent ⋮ \(\sigma_k\)-scalar curvature and eigenvalues of the Dirac operator ⋮ On a spin conformal invariant on manifolds with boundary ⋮ A Sobolev-like inequality for the Dirac operator ⋮ Lower bounds for eigenvalues of the Dirac operator on surfaces of rotation ⋮ Some explicit constructions of Dirac-harmonic maps ⋮ Surgery and the Spinorial τ-Invariant ⋮ Upper bounds for the first eigenvalue of the Dirac operator on surfaces ⋮ THE FIRST EIGENVALUE OF THE DIRAC OPERATOR IN A CONFORMAL CLASS ⋮ Conformal geometry and global invariants ⋮ Lower eigenvalue estimates for Dirac operators