相关论文: Eigenvalues and Holonomy

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 develop a Hellmann--Feynman type perturbation theory for the discrete signed $p$-Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues of the signed $p$-Laplacian can be characterized as citical…

The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description…

Let $G$ be a connected undirected graph with $n$, $n\ge 3$, vertices and $m$ edges. Denote by $\rho_1 \ge \rho_2 \ge \cdots > \rho_n =0$ the normalized Laplacian eigenvalues of $G$. Upper and lower bounds of $\rho_i$, $i=1,2,\ldots , n-1$,…

In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity…

We consider the Laplacian eigenvalues for smooth planar domains with strongly attractive Robin conditions imposed on a part of the boundary and Neumann condition on the remaining boundary. The asymptotics of individual eigenvalues is…

We characterize the relationship between the singular values of a complex Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of an Hermitian…

We study Hadamard's variational formula for simple eigenvalues under dynamical and conformal deformations. Particularly, harmonic convexity of the first eigenvalue of the Laplacian under the mixed boundary condition is established for…

The spectrum of the normalized graph Laplacian yields a very comprehensive set of invariants of a graph. In order to understand the information contained in those invariants better, we systematically investigate the behavior of this…

We propose the notion of normalized Laplacian matrix $\mathcal{L}(\Phi)$ for a gain graphs and study its properties in detail, providing insights and counterexamples along the way. We establish bounds for the eigenvalues of…

Determinants and symmetric functions of the eigenvalues of matrices characterizing stochastic processes with indepedent increments. Relationships with Fibonacci numbers are derived.

Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of…

We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…

The eigenvalues of the normalized Laplacian of a graph provide information on its topological and structural characteristics and also on some relevant dynamical aspects, specifically in relation to random walks. In this paper we determine…

We review a recent new approach to the study of critical points of Laplacian eigenfunctions. Its core novelty is a non-standard variational principle for the eigenvalues of the Laplacians with Neumann and Dirichlet boundary conditions on…

We determine a formula for the average values of L-series associated to eigenforms at complex values.

We consider quantum holonomy of some three-dimensional general covariant non-Abelian field theory in Landau gauge and confirm a previous result partially proven. We show that quantum holonomy retains metric independence after explicit gauge…

We consider the quantum mechanical hamiltonian of two, space indexed, hermitean matrices. By introducing matrix valued polar coordinates, we obtain the form of the laplacian acting on invariant states. For potentials depending only on the…

In this article, it is proved that the eigenvalue variety of the exterior of a nontrivial, non-Hopf, Brunnian link in $\mathbb{S}^{3}$ contains a nontrivial component of maximal dimension. This generalises, for Brunnian links, the…

We provide a partial answer to a question of Ekholm, Honda, and K\'alm\'an about the relationship between Khovanov homology and decomposable Lagrangian cobordisms. We also utilize previously defined filtered invariants to give obstructions…