Related papers: Eigenvalues and Holonomy

Let K be a field. For a given valuation on K[x], we determine the structure of its graded algebra and describe its set of key polynomials, in terms of any given key polynomial of minimal degree. We also characterize valuations not admitting…

We study the rate of convergence for (variational) eigenvalues of several non-linear problems involving oscillating weights and subject to different kinds of boundary conditions in bounded domains.

It is shown that a given non-autonomous system of two first-order ordinary differential equations can be expressed in Hamiltonian form. The derivation presented here allow us to obtain previously known results such as the infinite number of…

We extend the Otal-Rosas bound on the number of small eigenvalues of the Laplacian on a hyperbolic surface to the small eigenvalues of pseudo-Laplacians. In the process, we extend the work of Colin de Verdi\`ere on the spectral theory of…

In this paper, we introduce isocapacitary constants for the $p$-Laplacian on graphs and apply them to derive estimates for the first eigenvalues of the Dirichlet $p$-Laplacian, the Neumann $p$-Laplacian, and the $p$-Steklov problem.

It is known that the small eigenvalues of the Laplacian of a Riemann surface close to the boundary of the modular space can be well approximated by the eigenvalues of the discrete Laplacian on a certain graph coming from the pair of pants…

Laplacian matrices of weighted graphs in surfaces $S$ are used to define module and polynomial invariants of $Z/2$-homologically trivial links in $S \times [0,1]$. Information about virtual genus is obtained.

We revisit the eigenvalue problem of the Dirichlet Laplacian on bounded domains in complete Riemannian manifolds. By building on classical results like Li-Yau's and Yang's inequalities, we derive upper and lower bounds for eigenvalues. For…

Spectral hypergraph theory has recently attracted considerable interest as it provides a natural framework for modeling higher-order relationships beyond classical graphs. In this setting, eigenvalues of adjacency, Laplacian, and…

We describe the valuations following infinitely near singular points of a (singular) holomorphic foliation in the complex plane. They appear to be those satisfying a generalization of L'Hopital's rule. With them, we characterize dicritical…

In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…

In this paper we introduce the magnetic Hodge Laplacian, which is a generalization of the magnetic Laplacian on functions to differential forms. We consider various spectral results, which are known for the magnetic Laplacian on functions…

We consider the two-dimensional eigenvalue problem for the Laplacian with the Neumann boundary condition involving the critical Hardy potential. We prove the existence of the second eigenfunction and study its asymptotic behavior around the…

We provide explicit bounds on the eigenvalues of transfer operators defined in terms of holomorphic data.

We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.

Exploring the relationship between geometry and the resonant frequencies of a shape is of interest to pure and applied mathematicians. These resonant frequencies are related to the spectrum of the Laplacian, a partial differential operator.…

In this paper, we firstly consider Dirichlet eigenvalue problem which is related to Xin-Laplacian on the bounded domain of complete Riemannian manifolds. By establishing the general formulas, combining with some results of Chen and Cheng…

For a bounded domain $\Omega$ with a piecewise smooth boundary in an $n$-dimensional Euclidean space $\mathbf{R}^{n}$, we study eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. First we give a general inequality for…

We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In…

We explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive…