Related papers: Spectral optimisation of Dirac rectangles
We consider the Dirac operator on right triangles, subject to infinite-mass boundary conditions. We conjecture that the lowest positive eigenvalue is minimised by the isosceles right triangle both under the area or perimeter constraints. We…
We are concerned with the dependence of the lowest eigenvalue of the magnetic Dirichlet Laplacian on the geometry of rectangles, subject to homogeneous fields. We conjecture that the square is a global minimiser both under the area or…
Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We study the…
We study the minimization problem for eigenvalues of the Dirac operator within a fixed conformal class on a closed spin Riemannian manifold. We establish a criterion for the existence of a minimizer for this variational problem, focusing…
Consider a Dirac operator on an oriented compact surface endowed with a Riemannian metric and spin structure. Provided the area and the conformal class are fixed, how small can the $k$-th positive Dirac eigenvalue be? This problem mirrors…
We consider the self-adjoint Dirac operators on a finite interval with summable matrix-valued potentials and general boundary conditions. For such operators, we study the inverse problem of reconstructing the potential and the boundary…
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices…
We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets…
In this paper, we consider a problem for the first order Dirac differential equations system with spectral parameter dependent in boundary condition. The asymptotic behaviors of eigenvalues, eigenfunctions and normalizing numbers of this…
We consider a problem in eigenvalue optimization, in particular finding a local minimizer of the spectral abscissa - the value of a parameter that results in the smallest value of the largest real part of the spectrum of a matrix system.…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
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…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
Consider a convex function that is invariant under an group of transformations. If it has a minimizer, does it also have an invariant minimizer? Variants of this problem appear in nonparametric statistics and in a number of adjacent fields.…
We consider the problem of minimizing convex combinations of the first two eigenvalues of the Dirichlet-Laplacian among open sets of $R^N$ of fixed measure. We show that, by purely elementary arguments, based on the minimality condition, it…
We study the minimization of a spectral functional made as the sum of the first eigenvalue of the Dirichlet Laplacian and the relative strength of a Riesz-type interaction functional. We show that when the Riesz repulsion strength is below…
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…
We establish a sharp extrinsic lower bound for the first eigenvalue of the Dirac operator of an untrapped surface in initial data sets without apparent horizon in terms of the norm of its mean curvature vector. The equality case leads to…
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
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.