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Related papers: Boundary distortion estimates for holomorphic maps

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In this paper, we consider mappings on uniform domains with exponentially integrable distortion whose Jacobian determinants are integrable. We show that such mappings can be extended to the boundary and moreover these extensions are…

Complex Variables · Mathematics 2024-10-15 Tuomo Akkinen , Chang-Yu Guo

We establish an extension of Liouville's classical representation theorem for solutions of the partial differential equation $\Delta u=4 e^{2u}$ and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps…

Complex Variables · Mathematics 2014-02-26 Daniela Kraus , Oliver Roth

In this article we obtain large deviation estimates for zeros of random holomorphic sections on punctured Riemann surfaces. These estimates are then employed to yield estimates for the respective hole probabilities. A particular case of…

Complex Variables · Mathematics 2021-09-21 Alexander Drewitz , Bingxiao Liu , George Marinescu

There are many classical results, related to the Denjoy--Wolff Theorem, concerning the relationship between orbits of interior points and orbits of boundary points under iterates of holomorphic self-maps of the unit disc. Here, for the…

Dynamical Systems · Mathematics 2023-06-28 Anna Miriam Benini , Vasiliki Evdoridou , Núria Fagella , Philip J. Rippon , Gwyneth M. Stallard

For a large class of nonuniformly expanding maps of $\Bbb R^m$, with indifferent fixed points and unbounded distorsion and non necessarily Markovian, we construct an absolutely continuous invariant measure. We extend to our case techniques…

Dynamical Systems · Mathematics 2007-05-23 Huyi Hu , Sandro Vaienti

We consider a class of piecewise smooth one-dimensional maps with critical points and singularities (possibly with infinite derivative). Under mild summability conditions on the growth of the derivative on critical orbits, we prove the…

Dynamical Systems · Mathematics 2015-05-30 Stefano Luzzatto , Ian Melbourne

In this paper, we obtain upper estimates for the distortion of the modulus of families of paths under mappings of the Sobolev class, whose dilatation is locally integrable. As a consequence, theorems on the local and boundary behavior of…

Complex Variables · Mathematics 2019-04-18 E. Sevost'yanov

We introduce a new biharmonic Steklov problem on differential forms with Dirichlet-type boundary conditions and show that it is elliptic. We prove the existence of a discrete spectrum for this problem and give variational characterizations…

Differential Geometry · Mathematics 2026-02-11 Rodolphe Abou Assali

We study the angular derivative problem for petals of one-parameter semigroups of holomorphic self-maps of the unit disk. For hyperbolic petals we prove a necessary and sufficient condition for the conformality of the petal in terms of the…

Complex Variables · Mathematics 2024-01-09 Pavel Gumenyuk , Maria Kourou , Oliver Roth

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

Functional Analysis · Mathematics 2014-05-22 Ibrahim Karahan , Murat Ozdemir

We establish two-point distortion theorems for sense-preserving planar harmonic mappings $f=h+\overline{g}$ which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the…

Complex Variables · Mathematics 2022-08-08 Víctor Bravo , Rodrigo Hernández , Osvaldo Venegas

In this article, we consider the estimation of the marginal distributions for pairs of data are recorded, with unobserved order in each pair. New estimators are proposed and their asymptotic properties are established, by proving a…

Statistics Theory · Mathematics 2021-04-26 L. Dumitrescu , D. Harcourt

We investigate distortion estimates for mappings at boundary points of a domain. We consider mappings of the Sobolev and Orlicz-Sobolev classes and some other classes of mappings that do not preserve the boundary of a domain. For above…

Complex Variables · Mathematics 2026-03-17 Victoria Desyatka , Zarina Kovba , Evgeny Sevost'yanov

In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing…

Complex Variables · Mathematics 2018-01-08 Gang Liu , Saminathan Ponnusamy

We use quantum invariants to define an analytic family of representations for the mapping class group of a punctured surface. The representations depend on a complex number A with |A| <= 1 and act on an infinite-dimensional Hilbert space.…

Geometric Topology · Mathematics 2014-11-11 Francesco Costantino , Bruno Martelli

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

Complex Variables · Mathematics 2023-06-21 Giovanni Domenico Di Salvo

We prove the uniqueness of solutions to Dirichlet problem for p-harmonic maps with images in a small geodesic ball of the target manifold. As a consequence, we show that such maps have Hoelder continuous derivatives. This gives an extension…

Analysis of PDEs · Mathematics 2012-03-12 Ali Fardoun , Rachid Regbaoui

The construction of optimal non-uniform mappings for discrete input memoryless channels (DIMCs) is investigated. An efficient algorithm to find optimal mappings is proposed and the rate by which a target distribution is approached is…

Information Theory · Computer Science 2014-07-09 Georg Böcherer

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning…

Machine Learning · Computer Science 2026-01-27 Adrienne M. Propp , Jonas A. Actor , Elise Walker , Houman Owhadi , Nathaniel Trask , Daniel M. Tartakovsky

By the Riemann-mapping theorem, one can bijectively map the interior of an $n$-gon $P$ to that of another $n$-gon $Q$ conformally. However, (the boundary extension of) this mapping need not necessarily map the vertices of $P$ to those $Q$.…

Differential Geometry · Mathematics 2014-01-27 Mayank Goswami , Xianfeng Gu , Vamsi P. Pingali , Gaurish Telang