Conformal lower bounds for the Dirac operator of embedded hypersurfaces

DOI10.4310/AJM.2002.v6.n1.a2zbMath1016.58013MaRDI QIDQ700532

Oussama Hijazi, Xiao Zhang, Sebastían Montiel

Publication date: 22 October 2002

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

hypersurfaceDirac operatorYamabe problemconformal invariantsconformal lower boundsfirst nonnegative eigenvalue

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Global Riemannian geometry, including pinching (53C20)

Related Items (19)

Eigenvalue estimates for the Dirac operator with generalized APS boundary condition ⋮ A spinorial characterization of hyperspheres ⋮ Scalar flat compactifications of Poincaré-Einstein manifolds and applications ⋮ The Dirac operator on untrapped surfaces ⋮ The Dirac-Witten operator on pseudo-Riemannian manifolds ⋮ Dirac operators on noncommutative hypersurfaces ⋮ First boundary Dirac eigenvalue and boundary capacity potential ⋮ Spinorial proofs of the Alexandrov theorem for higher order mean curvatures in \(\mathbb{R}^{n + 1}\) and the Heintze-Karcher inequality ⋮ Estimates for solutions of Dirac equations and an application to a geometric elliptic-parabolic problem ⋮ Supersymmetric rigidity of asymptotically locally hyperbolic manifolds ⋮ Green functions for the Dirac operator under local boundary conditions and applications ⋮ Complex generalized Killing spinors on Riemannian \(\mathrm{Spin}^c\) manifolds ⋮ Uniqueness of the de Sitter spacetime among static vacua with positive cosmological constant ⋮ Eigenvalue estimate of the Dirac operator and rigidity of Poincaré-Einstein metrics ⋮ Spin\(^{c}\) geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian sub\-manifolds ⋮ The Hijazi inequality on manifolds with boundary ⋮ Rigidity of compact Riemannian spin manifolds with boundary ⋮ A holographic principle for the existence of imaginary Killing spinors ⋮ Optimal eigenvalues estimate for the Dirac operator on domains with boundary

This page was built for publication: Conformal lower bounds for the Dirac operator of embedded hypersurfaces