相关论文: Quasiconformal properties of $Q_{p,0}$ curves and …

Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…

The main question studied in this paper concerns the weak-coupling behavior of the geometrically induced bound states of singular Schr\"odinger operators with an attractive $\delta$ interaction supported by a planar, asymptotically straight…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

We show that every homeomorphic $W^{1,1}_{\rm loc}$ solution $f$ to a Beltrami equation $\bar{\partial}f=\mu \partial f$ in a domain $D\subset\Bbb C$ is the so--called lower $Q-$homeomorphism with $Q(z)=K^T_{\mu}(z, z_0)$ where…

Let $\Omega$ be a bounded domain of $\mathbb{R}^{n+1}$ with $n \ge 1$. We assume that the boundary $\Gamma$ of $\Omega$ is Lipschitz. Consider the Dirichlet-to-Neumann operator $N_0$ associated with a system in divergence form of size $m$…

Let $R$ be a compact Riemann surface and $\Gamma$ be a Jordan curve separating $R$ into connected components $\Sigma_1$ and $\Sigma_2$. We consider Calder\'on-Zygmund type operators $T(\Sigma_1,\Sigma_k)$ taking the space of $L^2$…

Let $\mathbb{P}^1$ and $(X,q)$ denote, respectively, the projective line and a fixed elliptic curve marked at its origin, both defined over an algebraically closed field $\mathbb{K}$ of arbitrary characteristic $\emph{\textbf{p}} \neq2$. We…

We establish the exact (up to the constants) double inequality for the Christoffel function for a measure supported on a Jordan domain bounded by a quasiconformal curve. We show that this quasiconformality of the boundary cannot be omitted.

The {\em metric dimension} of a graph $\Gamma$ is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph…

For a digraph $\Gamma$, if $F$ is the smallest field that contains all roots of the characteristic polynomial of the adjacency matrix of $\Gamma$, then $F$ is called the splitting field of $\Gamma$. The extension degree of $F$ over the…

We discuss the analogy between collapsing Conformal Field Theories and measured Gromov-Hausdorff limit of Riemannian manifolds with non-negative Ricci curvature. Motivated by this analogy we propose the notion of non-commutative…

We prove that the $n$th Chebyshev polynomial $T_{n}$ of a piecewise Dini-smooth Jordan curve $\Gamma$ satisfies \[ \lim_{n\to\infty}\frac{\|T_{n}\|_{\Gamma}}{\mathrm{cap}(\Gamma)^n}=1, \] where $\|\cdot\|_\Gamma$ is the supremum norm over…

We study piecewise quasiconformal covering maps of the unit circle. We provide sufficient conditions so that a conjugacy between two such dynamical systems has a quasiconformal or David extension to the unit disk. Our main result…

A quasiplane $f(V)$ is the image of an $n$-dimensional Euclidean subspace $V$ of ${\Bbb R}^N$ ($1\leq n\leq N-1$) under a quasiconformal map $f:{\Bbb R}^N\to{\Bbb R}^N$ . We give sufficient conditions in terms of the weak quasisymmetry…

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…

Consider a sequence of Riemannian manifolds $(M^n_i,g_i)$ with scalar curvatures and entropies bounded below by small constants $R_i,\mu_i \geq-\epsilon_i$. The goal of this paper is to understand notions of convergence and the structure of…

Let $\Gamma$ denote a distance-regular graph with diameter $D \ge 3$. Assume $\Gamma$ has classical parameters $(D,b,\alpha,\beta)$ with $b < -1$. Let $X$ denote the vertex set of $\Gamma$ and let $A \in MX$ denote the adjacency matrix of…

We study the eigenvalue problem for the Dirichlet Laplacian in bounded simply connected plane domains $\Omega\subset\mathbb{C}$ using conformal transformations of the original problem to the weighted eigenvalue problem for the Dirichlet…

For any integers $p\geq 2$ and $q\geq 1$, let $\mathbb{H}^{p,q}$ be the pseudo-Riemannian hyperbolic space of signature $(p,q)$. We prove that if $\Gamma$ is the fundamental group of a closed aspherical $p$-manifold, then the set of…

We prove that any metric space $X$ homeomorphic to $\mathbb{R}^2$ with locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on modulus of curve families associated to a quadrilateral. More precisely, let $Q \subset X$ be a…