Related papers: Dirac operators on hypersurfaces as large mass lim…
We consider the magnetic Dirac operator on a curved strip whose boundary carries the infinite mass boundary condition. When the magnetic field is large, we provide the reader with accurate estimates of the essential and discrete spectra. In…
We describe a new family of examples of hypersurfaces in the sphere satisfying the limiting-case in C. B\"ar's extrinsic upper bound for the smallest eigenvalue of the Dirac operator.
We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator on locally reducible spacelike submanifold in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied.
New extrinsic lower bounds are given for the classical Dirac operator on the boundary of a compact domain of a spin manifold. The main tool is to solve some boundary problems for the Dirac operator of the domain under boundary conditions of…
This paper is devoted to a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator. We prove an abstract theorem, then we apply it to the case of Dirac operators with a…
In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…
Under standard local boundary conditions or certain global APS boundary conditions, we get lower bounds for the eigenvalues of the Dirac operator on compact spin manifolds with boundary. Limiting cases are characterized by the existence of…
We derive bounds on the location of non-embedded eigenvalues of Dirac operators on the half-line with non-Hermitian $L^1$-potentials. The results are sharp in the non-relativistic or weak-coupling limit. In the massless case, the absence of…
The set of constraints under which the eigenvalues of the Dirac operator can play the role of the dynamical variables for Euclidean supergravity is derived. These constraints arise when the gauge invariance of the eigenvalues of the Dirac…
We investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the Laplacian on Euclidean domains of unit volume, under Dirichlet and Neumann boundary conditions, respectively. In a second part,…
We give new estimates for the eigenvalues of the hypersurface Dirac operator in terms of the intrinsic energy-momentum tensor, the mean curvature and the scalar curvature. We also discuss their limiting cases as well as the limiting cases…
The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…
In this note, we prove an optimal upper bound for the first Dirac eigenvalue of some hypersurfaces in Euclidean space by combining a positive mass theorem and the construction of quasi-spherical metrics. As a direct consequence of this…
We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain of $\mathbb{R}^2$. Motivated by spectral geometric inequalities, we prove a non-linear variational formulation to…
The Dirac operator, acting in three dimensions, is considered. Assuming that a large mass $m>0$ lies outside a smooth and bounded open set $\Omega\subset\R^3$, it is proved that its spectrum is approximated by the one of the Dirac operator…
We study the eigenvalue problem for a one-dimensional Dirac operator with a spatially varying ``mass'' term. It is well-known that when the mass function has the form of a kink, or \emph{domain wall}, transitioning between strictly positive…
In this paper, we study eigenvalue of linear fourth order elliptic operators in divergence form with Dirichlet boundary condition on a bounded domain in a compact Riemannian manifolds with boundary (possibly empty) and find a general…
We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem…
This paper is devoted to the mathematical investigation of the MIT bag model, that is the Dirac operator on a smooth and bounded domain with certain boundary conditions. We prove that the operator is self-adjoint and, when the mass goes to…
We consider modifications of the classical dbar-Neumann conditions that define Fredholm problems for the Spin_C Dirac operator. In part II, we use boundary layer methods to obtain subelliptic estimates for these boundary value problems.…