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

Feida Jiang; Saihua Cui; Gang Li

Displaying similar documents to “Nonexistence of entire positive solution for a conformal $k$ -Hessian inequality”

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.

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...

Car-Pólya and Gel’fond’s theorems for $_{q} [T]$

David Adam (2004)

Acta Arithmetica

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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 $d + δ_{g}$ ...

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...

Uniqueness of entire functions and fixed points

Xiao-Guang Qi, Lian-Zhong Yang (2010)

Annales Polonici Mathematici

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Let f and g be entire functions, n, k and m be positive integers, and λ, μ be complex numbers with |λ| + |μ| ≠ 0. We prove that ${(f ⁿ (z) (λ f^{m} (z) + μ))}^{(} k)$ must have infinitely many fixed points if n ≥ k + 2; furthermore, if ${(f ⁿ (z) (λ f^{m} (z) + μ))}^{(} k)$ and ${(g ⁿ (z) (λ g^{m} (z) + μ))}^{(} k)$ have the same fixed points with the same multiplicities, then either f ≡ cg for a constant c, or f and g assume certain forms provided that n > 2k + m* + 4, where m* is an integer that depends only on λ.

Convergence of Taylor series in Fock spaces

Haiying Li (2014)

Studia Mathematica

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It is well known that the Taylor series of every function in the Fock space $F_{α}^{p}$ converges in norm when 1 < p < ∞. It is also known that this is no longer true when p = 1. In this note we consider the case 0 < p < 1 and show that the Taylor series of functions in $F_{α}^{p}$ do not necessarily converge “in norm”.

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.

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 $𝔹$ .

Stević-Sharma type operators on Fock spaces in several variables

Lijun Ma, Zicong Yang (2024)

Czechoslovak Mathematical Journal

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Let $ϕ$ be an entire self-map of $ℂ^{N}$ , $u_{0}$ be an entire function on $ℂ^{N}$ and $𝐮 = (u_{1}, \dots, u_{N})$ be a vector-valued entire function on $ℂ^{N}$ . We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_{0}, 𝐮, ϕ}$ as follows: $- . 4 p t T_{u_{0}, 𝐮, ϕ} f = u_{0} \cdot f \circ ϕ + \sum_{i = 1}^{N} u_{i} \cdot \frac{\partial f}{\partial z_{i}} \circ ϕ .$ We investigate the boundedness and compactness of $T_{u_{0}, 𝐮, ϕ}$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_{0}, 𝐮, ϕ}$ are also characterized.

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.

A Note on Transcendental Power Series Mapping the Set of Rational Numbers into Itself

Diego Marques, Elaine Silva (2017)

Communications in Mathematics

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In this note, we prove that there is no transcendental entire function $f (z) \in ℚ [[z]]$ such that $f (ℚ) \subseteq ℚ$ and $den f (p / q) = F (q)$ , for all sufficiently large $q$ , where $F (z) \in ℤ [z]$ .

Entire functions of exponential type not vanishing in the half-plane $ℑ z > k$ , where $k > 0$

Mohamed Amine Hachani (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let $P (z)$ be a polynomial of degree $n$ having no zeros in $| z | < k$ , $k \leq 1$ , and let $Q (z) : = z^{n} \bar{P (1 / \bar{z})}$ . It was shown by Govil that if ${max}_{| z | = 1} | P^{'} (z) |$ and ${max}_{| z | = 1} | Q^{'} (z) |$ are attained at the same point of the unit circle $| z | = 1$ , then $max_{| z | = 1} | P^{'} (z) | \leq \frac{n}{1 + k^{n}} max_{| z | = 1} | P (z) | .$ The main result of the present article is a generalization of Govil’s polynomial inequality to a class of entire functions of exponential type.

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.

The CR Yamabe conjecture the case $n = 1$

Najoua Gamara (2001)

Journal of the European Mathematical Society

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Let $(M, θ)$ be a compact CR manifold of dimension $2 n + 1$ with a contact form $θ$ , and $L = (2 + 2 / n) Δ_{b} + R$ its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form $\tilde{θ}$ on $M$ conformal to $θ$ which has a constant Webster curvature. This problem is equivalent to the existence of a function $u$ such that $L u = u^{1 + 2 / n}$ , $u > 0$ on $M$ . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where $n \geq 2$ and $(M, θ)$ is not locally CR equivalent to the sphere $S^{2 n + 1}$ of $𝐂^{n}$ . In a join work with R. Yacoub, the CR Yamabe...

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.

Zeros of solutions of certain higher order linear differential equations

Hong-Yan Xu, Cai-Feng Yi (2010)

Annales Polonici Mathematici

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We investigate the exponent of convergence of the zero-sequence of solutions of the differential equation $f^{(k)} + a_{k - 1} (z) f^{(k - 1)} + \dots + a ₁ (z) f^{'} + D (z) f = 0$ , (1) where $D (z) = Q ₁ (z) e^{P ₁ (z)} + Q ₂ (z) e^{P ₂ (z)} + Q ₃ (z) e^{P ₃ (z)}$ , P₁(z),P₂(z),P₃(z) are polynomials of degree n ≥ 1, Q₁(z),Q₂(z),Q₃(z), $a_{j} (z)$ (j=1,..., k-1) are entire functions of order less than n, and k ≥ 2.

$1$ -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 “Nonexistence of entire positive solution for a conformal k -Hessian inequality”

Displaying similar documents to “Nonexistence of entire positive solution for a conformal $k$ -Hessian inequality”