Optimal Eigenvalue Estimate for the Dirac–Witten Operator on Bounded Domains with Smooth Boundary

2007/12/19 by Daniel Maerten
Mathematics · #Boundary (topology) #Boundary value problem #Bounded function #Dirac (video compression format) #Dirac operator #Eigenvalues and eigenvectors #Infimum and supremum #Lambda #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Norm (philosophy) #Numerical methods in inverse problems #Operator (biology) #Physics #Pure mathematics #Quantum mechanics #Spectral Theory in Mathematical Physics #math.DG

paper · pdf · doi:10.1007/s11005-008-0267-2

2007, 18 pages, submitted 02 June 2007

arxiv created 2007/12/19 · openalex publication_date 2008/10/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for the usual Dirac operator. The limiting cases are also investigated.

Citations

• Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
• The mass of an asymptotically flat manifold
• A new proof of the positive energy theorem