相关论文: Reducing essential eigenvalues in the boundary of …
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are…
We prove nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite type boundary points of smooth bounded pseudoconvex domains in…
The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of black holes, the formation of trapped…
A closed surface evolving under mean curvature flow becomes singular in finite time. Near the singularity, the surface resembles a self-shrinker, a surface that shrinks by dilations under mean curvature flow. If the singularity is modeled…
We obtain new lower and upper bounds for the numerical radius of a bounded linear operator $A$ on a complex Hilbert space, which refine the existing ones. In particular, if $w(A)$ and $\|A\|$ denote the numerical radius and operator norm of…
The interplay between disorder and quantum interference leads to a wide variety of physical phenomena including celebrated Anderson localization -- the complete absence of diffusive transport due to quantum interference between different…
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…
Let $M$ be an oriented geometrically finite hyperbolic manifold of infinite volume with dimension at least $3$. For all $k \geq 0$, we provide a lower bound on the $k$th eigenvalue of the Laplace-Beltrami operator of $M$ by the $k$th…
We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of…
In this paper, we present an explicit description for the boundary behavior of the Bergman kernel function, the Bergman metric, and the associated curvatures along certain sequences converging to an $h$-extendible boundary point.
We consider the question of, given operators $A$, $Z$ and a sequence of invertible operators $U_n\to Z$, whether the sequence $U_nAU_n^{-1}$ is bounded in norm, as well as generalizations of this where $U_nAU_n^{-1}$ is modified by some…
In this note, we define a bounded variant on the Hilbert projective metric on an infinite dimensional space $E$ and study the contraction properties of the projective maps associated with positive linear operators on $E$. More precisely, we…
We derive sharp bounds for three types of eigenvalue problems. First, we derive an upper bound for the first $p$-Dirichlet eigenvalue on conformally compact (CC) spaces. As a consequence, we show that for a class of CC submanifolds of…
This work is focused on the local eigenvalue statistics for the Anderson tight binding model with non-rank-one perturbations over the canopy tree, at large disorder. On the Hilbert space $\ell^2(\mathcal{C})$, where $ \mathcal{C} $ is the…
In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values…
We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this…
The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor…
We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in $\RR^2$, and finite segments thereof. The waveguide is a perturbation of a periodic strip in terms of a sequence of independent identically distributed random…
This note studies Arveson's curvature invariant for d-contractions specialized to the case d=1 of a single contraction operator on a Hilbert space. It establishes a formula which gives an easy-to-understand meaning for the curvature of a…
Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…