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

J. Ławrynowicz

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

Universal Taylor series, conformal mappings and boundary behaviour

Stephen J. Gardiner (2014)

Annales de l’institut Fourier

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A holomorphic function $f$ on a simply connected domain $Ω$ is said to possess a universal Taylor series about a point in $Ω$ if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta $K$ outside $Ω$ (provided only that $K$ has connected complement). This paper shows that this property is not conformally invariant, and, in the case where $Ω$ is the unit disc, that such functions have extreme angular boundary behaviour.

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 a theorem of Lindelof

Vladimir Ya. Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give a quasiconformal version of the proof for the classical Lindelof theorem: Let $f$ map the unit disk $𝔻$ conformally onto the inner domain of a Jordan curve $𝒞$ : Then $𝒞$ is smooth if and only if arg $f^{'} (z)$ has a continuous extension to $\bar{𝔻}$ . Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.

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 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...

Conformal harmonic forms, Branson–Gover operators and Dirichlet problem at infinity

Erwann Aubry, Colin Guillarmou (2011)

Journal of the European Mathematical Society

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For odd-dimensional Poincaré–Einstein manifolds $(X^{n + 1}, g)$ , we study the set of harmonic $k$ -forms (for $k < n / 2$ ) which are $C^{m}$ (with $m \in ℕ$ ) on the conformal compactification $\bar{X}$ of $X$ . This set is infinite-dimensional for small $m$ but it becomes finite-dimensional if $m$ is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology $H^{k} (\bar{X}, \partial \bar{X})$ and the kernel of the Branson–Gover [3] differential operators $(L_{k}, G_{k})$ on the conformal infinity $(\partial \bar{X}, [h_{0}])$ . We also relate the set of $C^{n - 2 k + 1} (Λ^{k} (\bar{X}))$ forms in the kernel of $d + δ_{g}$ ...

Mobius invariant Besov spaces on the unit ball of $ℂ^{n}$

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We give new characterizations of the analytic Besov spaces $B_{p}$ on the unit ball $𝔹$ of $ℂ^{n}$ in terms of oscillations and integral means over some Euclidian balls contained in $𝔹$ .

The almost Einstein operator for $(2, 3, 5)$ distributions

Katja Sagerschnig, Travis Willse (2017)

Archivum Mathematicum

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For the geometry of oriented $(2, 3, 5)$ distributions $(M,)$ , which correspond to regular, normal parabolic geometries of type $(G_{2}, P)$ for a particular parabolic subgroup $P < G_{2}$ , we develop the corresponding tractor calculus and use it to analyze the first BGG operator $Θ_{0}$ associated to the $7$ -dimensional irreducible representation of $G_{2}$ . We give an explicit formula for the normal connection on the corresponding tractor bundle and use it to derive explicit expressions for this operator. We also show that solutions...

The logarithmic capacity in $C^{n}$

S. Kołodziej (1988)

Annales Polonici Mathematici

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On sets of confluent and related mappings in the space $Y^{X}$

T. Maćkowiak (1976)

Colloquium Mathematicae

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Superapproximation of the partial derivatives in the space of linear triangular and bilinear quadrilateral finite elements

Dalík, Josef

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A method for the second-order approximation of the values of partial derivatives of an arbitrary smooth function $u = u (x_{1}, x_{2})$ in the vertices of a conformal and nonobtuse regular triangulation $𝒯_{h}$ consisting of triangles and convex quadrilaterals is described and its accuracy is illustrated numerically. The method assumes that the interpolant $Π_{h} (u)$ in the finite element space of the linear triangular and bilinear quadrilateral finite elements from $𝒯_{h}$ is known only.

Lightlike hypersurfaces of an indefinite Kaehler manifold of a quasi-constant curvature

Dae Ho Jin, Jae Won Lee (2019)

Communications in Mathematics

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We study lightlike hypersurfaces $M$ of an indefinite Kaehler manifold $\bar{M}$ of quasi-constant curvature subject to the condition that the characteristic vector field $ζ$ of $\bar{M}$ is tangent to $M$ . First, we provide a new result for such a lightlike hypersurface. Next, we investigate such a lightlike hypersurface $M$ of $\bar{M}$ such that (1) the screen distribution $S (T M)$ is totally umbilical or (2) $M$ is screen conformal.

Some results on quasi-t-dual Baer modules

Rachid Tribak, Yahya Talebi, Mehrab Hosseinpour (2023)

Commentationes Mathematicae Universitatis Carolinae

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Let $R$ be a ring and let $M$ be an $R$ -module with $S = {End}_{R} (M)$ . Consider the preradical $\bar{Z}$ for the category of right $R$ -modules Mod- $R$ introduced by Y. Talebi and N. Vanaja in 2002 and defined by $\bar{Z} (M) = ⋂ {U \leq M : M / U$ is small in its injective hull $}$ . The module $M$ is called quasi-t-dual Baer if $\sum_{ϕ \in ℑ} ϕ ({\bar{Z}}^{2} (M))$ is a direct summand of $M$ for every two-sided ideal $ℑ$ of $S$ , where ${\bar{Z}}^{2} (M) = \bar{Z} (\bar{Z} (M))$ . In this paper, we show that $M$ is quasi-t-dual Baer if and only if ${\bar{Z}}^{2} (M)$ is a direct summand of $M$ and ${\bar{Z}}^{2} (M)$ is a quasi-dual Baer module. It is also shown that any direct...

Extremal plurisubharmonic functions in $C^{N}$

Józef Siciak (1981)

Annales Polonici Mathematici

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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.

Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms

Liguang Liu, Dachun Yang (2009)

Studia Mathematica

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Let s ∈ ℝ, p ∈ (0,1] and q ∈ [p,∞). It is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from the Triebel-Lizorkin space $Ḟ_{p, q}^{s} (ℝ ⁿ)$ to a quasi-Banach space ℬ if and only if sup ${| | T (a) | |}_{ℬ}$ : a is an infinitely differentiable (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ < ∞, where the (p,q,s)-atom of $Ḟ_{p, q}^{s} (ℝ ⁿ)$ is as defined by Han, Paluszyński and Weiss.

$1$ -cocycles on the group of contactomorphisms on the supercircle $S^{1 | 3}$ generalizing the Schwarzian derivative

Boujemaa Agrebaoui, Raja Hattab (2016)

Czechoslovak Mathematical Journal

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The relative cohomology $H_{diff}^{1} (𝕂 (1 | 3), 𝔬𝔰𝔭 (2, 3); 𝒟_{λ, μ} (S^{1 | 3}))$ of the contact Lie superalgebra $𝕂 (1 | 3)$ with coefficients in the space of differential operators $𝒟_{λ, μ} (S^{1 | 3})$ acting on tensor densities on $S^{1 | 3}$ , is calculated in N. Ben Fraj, I. Laraied, S. Omri (2013) and the generating $1$ -cocycles are expressed in terms of the infinitesimal super-Schwarzian derivative $1$ -cocycle $s (X_{f}) = D_{1} D_{2} D_{3} (f) α_{3}^{1 / 2}$ , $X_{f} \in 𝕂 (1 | 3)$ which is invariant with respect to the conformal subsuperalgebra $𝔬𝔰𝔭 (2, 3)$ of $𝕂 (1 | 3)$ . In this work we study the supergroup case. We give an explicit construction of $1$ -cocycles...

Displaying similar documents to “On a class of quasi-conformal mappings with invariant boundary points, I. The class E Q and and the general extremal problem”

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