ﻻ يوجد ملخص باللغة العربية
The fundamental gap conjecture was recently proven by Andrews and Clutterbuck: for any convex domain in $R^n$ normalized to have unit diameter, the difference between the first two Dirichlet eigenvalues of the Laplacian is bounded below by that of the interval. In this work, we focus on the moduli spaces of simplices in all dimensions, and later specialize to the moduli space of Euclidean triangles. Our first theorem is a compactness result for the gap function on the moduli space of simplices in any dimension. Our second main result verifies a recent conjecture of Antunes-Freitas: for any Euclidean triangle normalized to have unit diameter, the fundamental gap is uniquely minimized by the equilateral triangle.
This paper studies the size of the minimal gap between any two consecutive eigenvalues in the Dirichlet and in the Neumann spectrum of the standard Laplace operator on the Sierpinski gasket. The main result shows the remarkable fact that this minimal
We consider the problem of finding universal bounds of isoperimetric or isodiametric type on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at the vertices, in terms of various analytical and combinatorial proper
We describe a numerical procedure to compute the so-called isospectral torus of finite gap sets, that is, the set of Jacobi matrices whose essential spectrum is composed of finitely many intervals. We also study numerically the convergence of specifi
The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly constrained by s
We consider a family ${mathcal{H}^varepsilon}_{varepsilon>0}$ of $varepsilonmathbb{Z}^n$-periodic Schrodinger operators with $delta$-interactions supported on a lattice of closed compact surfaces; within a minimal period cell one has $minmathbb{N}$ s