Asymptotically conformal classes and non-Strebel points

Guowu Yao

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Displaying similar documents to “Asymptotically conformal classes and non-Strebel points”

Lower quantization coefficient and the F-conformal measure

Mrinal Kanti Roychowdhury (2011)

Colloquium Mathematicae

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Let $F = f^{(i)} : 1 \leq i \leq N$ be a family of Hölder continuous functions and let $φ_{i} : 1 \leq i \leq N$ be a conformal iterated function system. Lindsay and Mauldin’s paper [Nonlinearity 15 (2002)] left an open question whether the lower quantization coefficient for the F-conformal measure on a conformal iterated funcion system satisfying the open set condition is positive. This question was positively answered by Zhu. The goal of this paper is to present a different proof of this result.

On the conformal gauge of a compact metric space

Matias Carrasco Piaggio (2013)

Annales scientifiques de l'École Normale Supérieure

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In this article we study the Ahlfors regular conformal gauge of a compact metric space $(X, d)$ , and its conformal dimension ${dim}_{A R} (X, d)$ . Using a sequence of finite coverings of $(X, d)$ , we construct distances in its Ahlfors regular conformal gauge of controlled Hausdorff dimension. We obtain in this way a combinatorial description, up to bi-Lipschitz homeomorphisms, of all the metrics in the gauge. We show how to compute ${dim}_{A R} (X, d)$ using the critical exponent $Q_{N}$ associated to the combinatorial modulus.

Conformal measures and matings between Kleinian groups and quadratic polynomials

Marianne Freiberger (2007)

Fundamenta Mathematicae

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Following results of McMullen concerning rational maps, we show that the limit set of matings between a certain class of representations of C₂ ∗ C₃ and quadratic polynomials carries δ-conformal measures, and that if the correspondence is geometrically finite then the real number δ is equal to the Hausdorff dimension of the limit set. Moreover, when f is the limit of a pinching deformation ${f_{t}}_{0 \leq t < 1}$ we give sufficient conditions for the dynamical convergence of $f_{t}$ .

On a class of quasi-conformal mappings with invariant boundary points, I. The class $E_{Q}$ and and the general extremal problem

J. Ławrynowicz (1969)

Annales Polonici Mathematici

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Separation properties for self-conformal sets

Yuan-Ling Ye (2002)

Studia Mathematica

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For a one-to-one self-conformal contractive system ${w_{j}}_{j = 1}^{m}$ on $ℝ^{d}$ with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to $0 < ℋ^{α} (K) < \infty$ . We give a simple proof of this result as well as discuss some further properties related to the separation condition.

Nonexistence of entire positive solution for a conformal $k$ -Hessian inequality

Feida Jiang, Saihua Cui, Gang Li (2020)

Czechoslovak Mathematical Journal

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In this paper, we study the nonexistence of entire positive solution for a conformal $k$ -Hessian inequality in $ℝ^{n}$ via the method of proof by contradiction.

Ward identities from recursion formulas for correlation functions in conformal field theory

Alexander Zuevsky (2015)

Archivum Mathematicum

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A conformal block formulation for the Zhu recursion procedure in conformal field theory which allows to find $n$ -point functions in terms of the lower correlations functions is introduced. Then the Zhu reduction operators acting on a tensor product of VOA modules are defined. By means of these operators we show that the Zhu reduction procedure generates explicit forms of Ward identities for conformal blocks of vertex operator algebras. Explicit examples of Ward identities for the Heisenberg...

Four-dimensional Einstein metrics from biconformal deformations

Paul Baird, Jade Ventura (2021)

Archivum Mathematicum

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Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal to the foliation. Four-manifolds endowed with a conformal foliation by surfaces present a natural context to put into effect this process. We develop the tools to calculate the transformation of the Ricci curvature under such deformations and apply our method to construct Einstein $4$ -manifolds. Examples of one particular family have ends which collapse...

Conformal blocks and cohomology in genus 0

Prakash Belkale, Swarnava Mukhopadhyay (2014)

Annales de l’institut Fourier

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We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus $0$ for classical Lie algebras and $G_{2}$ .

Factorization of point configurations, cyclic covers, and conformal blocks

Michele Bolognesi, Noah Giansiracusa (2015)

Journal of the European Mathematical Society

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We describe a relation between the invariants of $n$ ordered points in projective $d$ -space and of points contained in a union of two linear subspaces. This yields an attaching map for GIT quotients parameterizing point configurations in these spaces, and we show that it respects the Segre product of the natural GIT polarizations. Associated to a configuration supported on a rational normal curve is a cyclic cover, and we show that if the branch points are weighted by the GIT linearization...

Volume and area renormalizations for conformally compact Einstein metrics

Graham, Robin C.

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Let $X$ be the interior of a compact manifold $\bar{X}$ of dimension $n + 1$ with boundary $M = \partial X$ , and $g_{+}$ be a conformally compact metric on $X$ , namely $\bar{g} \equiv r^{2} g_{+}$ extends continuously (or with some degree of smoothness) as a metric to $X$ , where $r$ denotes a defining function for $M$ , i.e. $r > 0$ on $X$ and $r = 0$ , $d r \neq 0$ on $M$ . The restrction of $\bar{g}$ to $T M$ rescales upon changing $r$ , so defines invariantly a conformal class of metrics on $M$ , which is called the conformal infinity of $g_{+}$ . In the present paper, the author considers conformally compact...