Lower bounds for the eigenvalues of the spin\(^{c}\) Dirac-Witten operator
type: Item
instance of: scholarly article
title: Lower bounds for the eigenvalues of the spin\(^{c}\) Dirac-Witten operator
zbMATH Open document ID: 1241.53040
published in: Science China. Mathematics
publication date: 2012-03-29T00:00:00Z
review text: The author derives optimal lower bounds for the eigenvalues of the spin\(^c\) Dirac-Witten operator on spin\(^c\) space-like hypersurfaces in an \((n+1)\)-dimensional Lorentzian manifold. These estimates involve the mean curvature, the scalar curvature, the first eigenvalue of the perturbed Yamabe operator, and the spinorial energy-momentum tensor. Other limiting cases involving conformal lower bounds, and compact hypersurfaces with non-empty boundary are discussed. Contents include: Introduction; Preliminaries; Lower bounds for the eigenvalues; Conformal lower bounds; Compact hypersurfaces with non-empty boundary, and References (twenty-six items).
Mathematics Subject Classification ID: 53C27
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C60
zbMATH DE Number: 6019639
zbMATH Keywords: spin\(^c\) Dirac-Witten operators
zbMATH Keywords: eigenvalues
zbMATH Keywords: mean and scalar curvature
zbMATH Keywords: conformal lower bounds
author: Yongfa Chen
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
full work available at URL: s11425-011-4240-7
OpenAlex ID: W2034820194
cites work: Zero sets of solutions to semilinear elliptic systems of first order
cites work: Q3668451
cites work: Lower bounds for eigenvalues of the Dirac-Witten operator
cites work: On eigenvalue estimates for the Dirac-Witten-type operators
cites work: Der erste Eigenwert des Dirac‐Operators einer kompakten, Riemannschen Mannigfaltigkeit nichtnegativer Skalarkrümmung
cites work: Generalized Killing spinors and conformal eigenvalue estimates for \(\text{Spin}^c\) manifolds
cites work: A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors
cites work: Q3985740
cites work: Lower bounds for the eigenvalues of the Dirac operator
cites work: Eigenvalues of the Dirac operator on manifolds with boundary
cites work: Lower bounds for the eigenvalues of the Dirac operator. I: The hypersurface Dirac operator
cites work: The Dirac-Witten operator on spacelike hypersurfaces
cites work: On the relation between ADM and Bondi energy-momenta. III: perturbed radiative spatial infinity
cites work: Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary
cites work: Eigenvalue estimates for the Dirac-Schröder operators
cites work: Parallel and Killing spinors on \(\text{Spin}^ c\) manifolds
cites work: Lower bounds for the eigenvalues of the Dirac operator on Spin\(^c\) manifolds
cites work: On Witten's proof of the positive energy theorem
cites work: A new proof of the positive energy theorem.
cites work: Lower bounds for eigenvalues of hypersurface Dirac operators
cites work: Positive mass conjecture for five-dimensional Lorentzian manifolds
cites work: Positive mass theorem for hypersurface in 5-dimensional Lorentzian manifolds
cites work: A quasi-local mass for 2-spheres with negative Gauss curvature
DOI: 10.1007/S11425-011-4240-7
description: scientific article; zbMATH DE number 6019639