Continuity of the relative extremal function on analytic varieties in ℂⁿ

Frank Wikström

Displaying similar documents to “Continuity of the relative extremal function on analytic varieties in ℂⁿ”

A new necessary condition for analytic varieties satisfying the local Phragmén-Lindelöf condition

Tobias Heinrich (2005)

Annales Polonici Mathematici

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For an analytic variety V in ℂⁿ containing the origin which satisfies the local Phragmén-Lindelöf condition $P L_{l o c} (0)$ it is shown that for each real simple curve γ and each d ≥ 1 the limit variety $T_{γ, d} V$ satisfies the strong Phragmén-Lindelöf condition (SPL).

The finiteness of compact varieties in $C^{n}$

Walter Rudin (1981)

Annales Polonici Mathematici

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Extremal plurisubharmonic functions in $C^{N}$

Józef Siciak (1981)

Annales Polonici Mathematici

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On the dimension of secant varieties

Luca Chiantini, Ciro Ciliberto (2010)

Journal of the European Mathematical Society

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In this paper we generalize Zak’s theorems on tangencies and on linear normality as well as Zak’s definition and classification of Severi varieties. In particular we find sharp lower bounds for the dimension of higher secant varieties of a given variety $X$ under suitable regularity assumptions on $X$ , and we classify varieties for which the bound is attained.

Asymptotics of eigensections on toric varieties

A. Huckleberry, H. Sebert (2013)

Annales de l’institut Fourier

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Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $| ϕ_{n} |^{2} = | s_{N} |^{2} / | | s_{N} {| |}_{L^{2}}^{2}$ for eigensections $s_{N} \in Γ (X, L^{N})$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate...

Lagrangian fibrations on generalized Kummer varieties

Martin G. Gulbrandsen (2007)

Bulletin de la Société Mathématique de France

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We investigate the existence of Lagrangian fibrations on the generalized Kummer varieties of Beauville. For a principally polarized abelian surface $A$ of Picard number one we find the following: The Kummer variety $K^{n} A$ is birationally equivalent to another irreducible symplectic variety admitting a Lagrangian fibration, if and only if $n$ is a perfect square. And this is the case if and only if $K^{n} A$ carries a divisor with vanishing Beauville-Bogomolov square.

The analytic $α$ -capacity and the Cauchy integral

K. Adžievski (1986)

Matematički Vesnik

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Real and complex analytic sets. The relevance of Segre varieties

Klas Diederich, Emmanuel Mazzilli (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X \subset {ℂ^{n}}^{n}$ be a closed real-analytic subset and put $𝒜 : = {z \in X ∣ \exists A \subset X, germ of a complex-analytic set, z \in A, {dim}_{z} A > 0}$ This article deals with the question of the structure of $𝒜$ . In the main result a natural proof is given for the fact, that $𝒜$ always is closed. As a main tool an interesting relation between complex analytic subsets of $X$ of positive dimension and the Segre varieties of $X$ is proved and exploited.

Interpolating discrete multiplicity varieties for $A ⁰_{p} (ℂ ⁿ)$

Bao Qin Li, Enrique Villamor (2006)

Studia Mathematica

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A necessary and sufficient condition is obtained for a discrete multiplicity variety to be an interpolating variety for the space $A ⁰_{p} (ℂ ⁿ)$ .

Finiteness of cominuscule quantum $K$ -theory

Anders S. Buch, Pierre-Emmanuel Chaput, Leonardo C. Mihalcea, Nicolas Perrin (2013)

Annales scientifiques de l'École Normale Supérieure

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The product of two Schubert classes in the quantum $K$ -theory ring of a homogeneous space $X = G / P$ is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on $X$ . We show that if $X$ is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to $X$ that take the marked points to general Schubert varieties and...

Equivariant K-theory of flag varieties revisited and related results

V. Uma (2013)

Colloquium Mathematicae

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We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring $K_{T} (G / B)$ of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in $K_{T} (G / B)$ to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of $K {(X)}_{ℚ}$ where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure...

Categorical equivalences of varieties generated by algebras $𝔄$ and $𝔄^{r}$

K. Denecke (1988)

Banach Center Publications

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Extremal sections of complex $l_{p}$ -balls, 0 < p ≤ 2

Alexander Koldobsky, Marisa Zymonopoulou (2003)

Studia Mathematica

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We study the extremal volume of central hyperplane sections of complex n-dimensional $l_{p}$ -balls with 0 < p ≤ 2. We show that the minimum corresponds to hyperplanes orthogonal to vectors ξ = (ξ¹,...,ξⁿ) ∈ ℂⁿ with |ξ¹| = ... = |ξⁿ|, and the maximum corresponds to hyperplanes orthogonal to vectors with only one non-zero coordinate.

Separately analytic functions and envelopes of holomorphy of some lower dimensional subsets of $C^{n}$

J. Siciak (1969)

Annales Polonici Mathematici

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The logarithmic capacity in $C^{n}$

S. Kołodziej (1988)

Annales Polonici Mathematici

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Radii of p-valence of certain analytic functions of order $α$ with negative coefficients

M. K. Aouf (1989)

Matematički Vesnik

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Solutions of non-homogeneous linear differential equations in the unit disc

Ting-Bin Cao, Zhong-Shu Deng (2010)

Annales Polonici Mathematici

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The main purpose of this paper is to consider the analytic solutions of the non-homogeneous linear differential equation $f^{(k)} + a_{k - 1} (z) f^{(k - 1)} + \dots + a ₁ (z) f^{'} + a ₀ (z) f = F (z)$ , where all coefficients $a ₀, a ₁, . . ., a_{k - 1}$ , F ≢ 0 are analytic functions in the unit disc = z∈ℂ: |z|<1. We obtain some results classifying the growth of finite iterated order solutions in terms of the coefficients with finite iterated type. The convergence exponents of zeros and fixed points of solutions are also investigated.

k-Normalization and (k+1)-level inflation of varieties

Valerie Cheng, Shelly Wismath (2008)

Discussiones Mathematicae - General Algebra and Applications

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Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety...

Convexity of sublevel sets of plurisubharmonic extremal functions

Finnur Lárusson, Patrice Lassere, Ragnar Sigurdsson (1998)

Annales Polonici Mathematici

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Let X be a convex domain in ℂⁿ and let E be a convex subset of X. The relative extremal function $u_{E, X}$ for E in X is the supremum of the class of plurisubharmonic functions v ≤ 0 on X with v ≤ -1 on E. We show that if E is either open or compact, then the sublevel sets of $u_{E, X}$ are convex. The proof uses the theory of envelopes of disc functionals and a new result on Blaschke products.

Inclusion and neighborhood properties of certain subclasses of p-valent functions of complex order defined by convolution

R. M. El-Ashwah, M. K. Aouf, S. M. El-Deeb (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we introduce and investigate three new subclasses of $p$ -valent analytic functions by using the linear operator $D_{λ, p}^{m} (f * g) (z)$ . The various results obtained here for each of these function classes include coefficient bounds, distortion inequalities and associated inclusion relations for $(n, θ)$ -neighborhoods of subclasses of analytic and multivalent functions with negative coefficients, which are defined by means of a non-homogenous differential equation.

Algebraic and analytic properties of solutions of abstract differential equations

R. Bittner

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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions....................................................................................................................................

Local analytic solutions of the functional equation $Φ (z) = H (z; Φ [f_{1} (z)], . . ., Φ [f_{m} (z)])$

Wilhelmina Smajdor (1970)

Annales Polonici Mathematici

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On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Jagannath Patel, Ashok Kumar Sahoo (2014)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The object of the present paper is to solve Fekete-Szego problem and determine the sharp upper bound to the second Hankel determinant for a certain class $R^{λ} (a, c, A, B)$ of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass ${\tilde{R}}^{λ} (a, c, A, B)$ of $R^{λ} (a, c, A, B)$ and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.