相关论文: Hyperbolic distance and membership of conformal ma…

Let $ S $ be a hyperbolic surface. We investigate the topology of the space of all curves on $ S $ which start and end at given points in given directions, and whose curvatures are constrained to lie in a given interval $…

A graph G is a (Euclidean) unit disk graph if it is the intersection graph of unit disks in the Euclidean plane $\mathbb{R}^2$. Recognizing them is known to be $\exists\mathbb{R}$-complete, i.e., as hard as solving a system of polynomial…

We prove a sharp $L^p$ weighted Hardy inequality involving boundary distance $\delta$ for any domain $\Omega\subsetneq \mathbb R^n$. The inequality may be improved substantially under the additional assumption that $-\log \delta$ is…

We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is…

Let $\alpha>-1$ and assume that $f$ is $\alpha-$harmonic mapping defined in the unit disk that belongs to the Hardy class $h^p$ with $p\ge 1$. We obtain some sharp estimates of the type $|f(z)|\le g(|r|) \|f^\ast\|_p$ and $|Df(z)|\le…

We study the $l_p$ Hausdorff distance from convex hull of a compact set $A\subset\mathbb{R}^n$, which is the distance \begin{equation*} d^{(l_p)}(A):=\sup_{x\in conv(A)}\inf_{a\in A}\|x-a\|_p, \end{equation*} where $\|\cdot\|_p$ is the…

We define a scale of Hardy spaces $\mathcal{H}^{p}_{FIO}(\mathbb{R}^{n})$, $p\in[1,\infty]$, that are invariant under suitable Fourier integral operators of order zero. This builds on work by Smith for $p=1$. We also introduce a notion of…

A new proof is given of the atomic decomposition of Hardy spaces Hp, in the classical setting of Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general setting and non classical settings.

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic,…

We prove that a backward orbit with bounded Kobayashi step for a hyperbolic or strongly elliptic holomorphic self-map of a bounded strongly convex domain in the d-dimensional complex Euclidean space necessarily converges to a boundary fixed…

A group $\Gamma$ with a family of subgroups $\mathbb{P}$ is relatively hyperbolic if $\Gamma$ admits a cusp-uniform action on a proper $\delta$--hyperbolic space. We show that any two such spaces for a given group pair are quasi-isometric,…

For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an atomic decomposition of these spaces in terms of reproducing kernels. We show that an…

Let $\mathcal{P}$ be a packing of circular disks of radius $\rho>0$ in the Euclidean, spherical, or hyperbolic plane. Let $0\leq\lambda\leq\rho$. We say that $\mathcal{P}$ is a $\lambda$-separable packing of circular disks of radius $\rho$…

We prove that the space $\mathcal{H}_\infty$ of framed infinite volume hyperbolic $3$-manifolds is connected but not path connected. Two proofs of connectivity of this space, which is equipped with the geometric topology, are given, each…

In this article, we give a short proof of Hardy's inequality for Hermite expansions of functions in the classical Hardy spaces $H^p({\mathbb R^n})$, by using an atomic decomposition of the Hardy spaces associated with the Hermite operators.…

In [2], the authors develop a global correspondence between immersed weakly horospherically convex hypersurfaces $\phi:M^n \to \mathbb{H}^{n+1}$ and a class of conformal metrics on domains of the round sphere $\mathbb{S}^n$. Some of the key…

Let psi: R^n --> R^k be a map defined by k positive definite quadratic forms on R^n. We prove that the relative entropy (Kullback-Leibler) distance from the convex hull of the image of psi to the image of psi is bounded above by an absolute…

Let $\Gamma$ be a geometrically-finite Fuchsian group acting on the upper half plane $\hh.$ Let $\E$ denote the set of elliptic fixed points of $\Gamma$ in $\hh.$ We give a lower bound on the minimal hyperbolic distance between points in…

Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function satisfying the globally log-H\"older continuous condition. In this article, the authors first obtain a decomposition for any distribution of the variable weak Hardy…

The aim of this article is to give a complete solution to the problem of the bilinear decompositions of the products of some Hardy spaces $H^p(\mathbb{R}^n)$ and their duals in the case when $p<1$ and near to $1$, via wavelets, paraproducts…