相关论文: The covering spectrum of a compact length space

On compact Riemannian manifolds with a large isometry group we investigate the invariant spectrum of the ordinary Laplacian. For either a toric Kaehler metric, or a rotationally-symmetric metric on the sphere, we produce upper bounds for…

For a Riemannian covering $\pi\colon M_1\to M_0$, the bottoms of the spectra of $M_0$ and $M_1$ coincide if the covering is amenable. The converse implication does not always hold. Assuming completeness and a lower bound on the Ricci…

The black hole area spectrum has been studied in the framework of tunneling mechanism, where a Generalized Uncertainty Principle (GUP) has been considered. The results implies in a non evenly spaced spectrum for the black hole area which…

To every Hermitian vector bundle with connection over a compact Riemannian manifold $M$ one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent…

This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…

We consider sequences of open Riemannian manifolds with boundary that have no regularity conditions on the boundary. To define a reasonable notion of a limit of such a sequence, we examine "$\delta$ inner regions" which avoid the boundary…

In this article, we continue the discussion of Fang-Wu (2015) to estimate the spectral gap of the Ornstein-Uhlenbeck operator on path space over a Riemannian manifold of pinched Ricci curvature. Along with explicit estimates we study the…

We formulate a qualitative argument, based on Heisenberg's uncertainty principle, to support the claim that when the effects of matter fields are assumed to overshadow the effects of quantum mechanics of spacetime, the discrete spectrum of…

In this paper, we extend the sharp lower bounds of spectal gap, due to Chen- Wang [10, 11], Bakry-Qian [6] and Andrews-Clutterbuck [5], from smooth Riemaniannian manifolds to general metric measure spaces with Riemannian curvature-dimension…

We define a metric on the class of metric spectral triples, which is null exactly between spectral triples with unitary equivalent Dirac operators and *-isomorphic underlying C*-algebras. This metric dominates the propinquity, and thus…

We analyse the spatial diversity of a multipath fading process for a finite region or curve in the plane. By means of the Karhunen-Lo\`eve (KL) expansion, this diversity can be characterised by the eigenvalue spectrum of the spatial…

Symmetric R-spaces can be characterized as real forms of Hermitian symmetric spaces, and as such, they are all embedded as Lagrangian submanifolds. We show that their maximal Weinstein tubular neighborhoods are dense and use this property…

We describe a new, short proof of some facts relating the gap lengths of the spectrum of a potential of Hill's equation to its regularity. For example, a real potential is in a weighted Gevrey-Sobolev space if and only if its gap lengths…

We consider a family of quantum graphs $\{(\Gamma,\mathcal{A}_\varepsilon)\}_{\varepsilon>0}$, where $\Gamma$ is a $\mathbb{Z}^n$-periodic metric graph and the periodic Hamiltonian $\mathcal{A}_\varepsilon$ is defined by the operation…

We provide new results on combinatorial characterizations of covering properties in end spaces and ray spaces. In particular, we characterize the Lindel\"of degree, the extent, the Rothberger property, $\sigma$-compactness and the Menger…

It is proved that small periodic singular perturbation of a cylindrical waveguide surface may open a gap in the continuous spectrum of the Dirichlet problem for the Laplace operator. If the perturbation period is long and the caverns in the…

We investigate the spectra of a family of pairs (M_i,A_i) consisting of a complete Riemannian manifold M_i and a closed subset A_i and which converge in the Lipschitz topology to a pair (M,A). This is used to construct manifolds of bounded…

Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as…

In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings…

On a compact metric graph, we consider the spectrum of the Laplacian defined with a mix of standard and Dirichlet vertex conditions. A Cheeger-type lower bound on the gap $\lambda_2 - \lambda_1$ is established, with a constant that depends…