Contact and conformal maps on Iwasawa N groups

Michael Cowling; Filippo De Mari; Adam Korányi; Hans Martin Reimann

Displaying similar documents to “Contact and conformal maps on Iwasawa N groups”

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.

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.

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.

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.

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 $f_{t}$ .

Asymptotically conformal classes and non-Strebel points

Guowu Yao (2016)

Studia Mathematica

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Let T(Δ) be the universal Teichmüller space on the unit disk Δ and T₀(Δ) be the set of asymptotically conformal classes in T(Δ). Suppose that μ is a Beltrami differential on Δ with [μ] ∈ T₀(Δ). It is an interesting question whether [tμ] belongs to T₀(Δ) for general t ≠ 0, 1. In this paper, it is shown that there exists a Beltrami differential μ ∈ [0] such that [tμ] is a non-trivial non-Strebel point for any $t \in (- 1 / | | μ | |_{\infty}, 1 / | | μ | |_{\infty}) ∖ 0, 1$ .

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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Conformal Killing graphs in foliated Riemannian spaces with density: rigidity and stability

Marco L. A. Velásquez, André F. A. Ramalho, Henrique F. de Lima, Márcio S. Santos, Arlandson M. S. Oliveira (2021)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we investigate the geometry of conformal Killing graphs in a Riemannian manifold ${\bar{M}}_{f}^{n + 1}$ endowed with a weight function $f$ and having a closed conformal Killing vector field $V$ with conformal factor $ψ_{V}$ , that is, graphs constructed through the flow generated by $V$ and which are defined over an integral leaf of the foliation $V^{⊥}$ orthogonal to $V$ . For such graphs, we establish some rigidity results under appropriate constraints on the $f$ -mean curvature. Afterwards, we obtain some stability...

The groups of automorphisms of the Witt $W_{n}$ and Virasoro Lie algebras

Vladimir V. Bavula (2016)

Czechoslovak Mathematical Journal

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Let $L_{n} = K [x_{1}^{\pm 1}, ..., x_{n}^{\pm 1}]$ be a Laurent polynomial algebra over a field $K$ of characteristic zero, $W_{n} : = {Der}_{K} (L_{n})$ the Lie algebra of $K$ -derivations of the algebra $L_{n}$ , the so-called Witt Lie algebra, and let $Vir$ be the Virasoro Lie algebra which is a $1$ -dimensional central extension of the Witt Lie algebra. The Lie algebras $W_{n}$ and $Vir$ are infinite dimensional Lie algebras. We prove that the following isomorphisms of the groups of Lie algebra automorphisms hold: ${Aut}_{Lie} (Vir) ≃ {Aut}_{Lie} (W_{1}) ≃ {\pm 1} ⋉ K^{*}$ , and give a short proof that ${Aut}_{Lie} (W_{n}) ≃ {Aut}_{K - alg} (L_{n}) ≃ {GL}_{n} (ℤ) ⋉ K^{* n}$ .

On $g$ -natural conformal vector fields on unit tangent bundles

Mohamed Tahar Kadaoui Abbassi, Noura Amri (2021)

Czechoslovak Mathematical Journal

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We study conformal and Killing vector fields on the unit tangent bundle, over a Riemannian manifold, equipped with an arbitrary pseudo-Riemannian $g$ -natural metric. We characterize the conformal and Killing conditions for classical lifts of vector fields and we give a full classification of conformal fiber-preserving vector fields on the unit tangent bundle endowed with an arbitrary pseudo-Riemannian Kaluza-Klein type metric.

Two-spinor tetrad and Lie derivatives of Einstein-Cartan-Dirac fields

Daniel Canarutto (2018)

Archivum Mathematicum

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An integrated approach to Lie derivatives of spinors, spinor connections and the gravitational field is presented, in the context of a previously proposed, partly original formulation of a theory of Einstein-Cartan-Maxwell-Dirac fields based on “minimal geometric data”: the needed underlying structure is determined, via geometric constructions, from the unique assumption of a complex vector bundle $S M$ with 2-dimensional fibers, called a $2$ -spinor bundle. Any further considered object is...

$q$ -difference conformal invariant operators and equations

Dobrev, V. K.

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More on tie-points and homeomorphism in ℕ*

Alan Dow, Saharon Shelah (2009)

Fundamenta Mathematicae

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A point x is a (bow) tie-point of a space X if X∖x can be partitioned into (relatively) clopen sets each with x in its closure. We denote this as $X = A ⋈_{x} B$ where A, B are the closed sets which have a unique common accumulation point x. Tie-points have appeared in the construction of non-trivial autohomeomorphisms of βℕ = ℕ* (by Veličković and Shelah Steprans) and in the recent study (by Levy and Dow Techanie) of precisely 2-to-1 maps on ℕ*. In these cases the tie-points have been the unique...