Lower bounds for the eigenvalues of the Dirac operator. I: The hypersurface Dirac operator

DOI10.1023/A:1010749808691zbMath0989.53030OpenAlexW6337041MaRDI QIDQ5943917

Oussama Hijazi, Xiao Zhang

Publication date: 19 September 2001

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1010749808691

zbMATH Keywords

Dirac operatorAtiyah-Singer index theorybounds on eigenvaluesYamabe number

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27) Global submanifolds (53C40)

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Eigenvalue estimates for the Dirac operator with generalized APS boundary condition ⋮ Extrinsic conformal lower bounds of eigenvalue for Dirac operator ⋮ Lower bounds for the eigenvalue estimates of the submanifold Dirac operator ⋮ Lower eigenvalue estimates of a Dirac-type operator involving electromagnetic field ⋮ Limiting case of the spin hypersurface Dirac operator arising in the positive mass theorem for black holes ⋮ Generalization of Kim's estimates in terms of the trace of divergence‐free symmetric tensor ⋮ The Dirac-Witten operator on pseudo-Riemannian manifolds ⋮ On the spectrum of spherical Dirac-type operators ⋮ A new quasi-local mass and positivity ⋮ Eigenvalue estimates for the Dirac-Schröder operators ⋮ Eigenvalue estimate of the Dirac operator and rigidity of Poincaré-Einstein metrics ⋮ Lower bounds for the eigenvalues of the spin\(^{c}\) Dirac-Witten operator ⋮ Some estimates over spacelike spin hypersurfaces of Lorentzian manifold ⋮ Lower bounds for eigenvalues of the Dirac-Witten operator ⋮ Lower bounds for the eigenvalues of the \(\mathrm{Spin}^c\) Dirac operator on submanifolds ⋮ Estimation on the Spin${}^c$ twisted Dirac operators

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