Diametral dimension of some pseudoconvex multiscale spaces

Jean-Marie Aubry; Françoise Bastin

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Displaying similar documents to “Diametral dimension of some pseudoconvex multiscale spaces”

The equation $\bar{\partial}u=f$ the intersection of pseudoconvex domains

Alessandro Perotti (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Viene studiata l'equazione $\bar{\partial}u=f$ per le forme regolari sulla chiusura dell'intersezione di $k$ domini pseudoconvessi. Si costruisce un operatore soluzione in forma integrale e sotto ipotesi opportune si ottengono stime della soluzione nelle norme $\mathbf{C}^{k}$ .

Small sets in $C^{n}$

Urban Cegrell (1985)

Annales Polonici Mathematici

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Rigidity of CR morphisms between compact strongly pseudoconvex CR manifolds

Stephen S.-T. Yau (2011)

Journal of the European Mathematical Society

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Let $X_{1}$ and $X_{2}$ be two compact strongly pseudoconvex CR manifolds of dimension $2 n - 1 \geq 5$ which bound complex varieties $V_{1}$ and $V_{2}$ with only isolated normal singularities in $ℂ^{N 1}$ and $ℂ^{N 2}$ respectively. Let $S_{1}$ and $S_{2}$ be the singular sets of $V_{1}$ and $V_{2}$ respectively and $S_{2}$ is nonempty. If $2 n - N_{2} - 1 \geq 1$ and the cardinality of $S_{1}$ is less than 2 times the cardinality of $S_{2}$ , then we prove that any non-constant CR morphism from $X_{1}$ to $X_{2}$ is necessarily a CR biholomorphism. On the other hand, let $X$ be a compact strongly pseudoconvex CR...

The equation $\bar{\partial}u=f$ the intersection of pseudoconvex domains

Alessandro Perotti (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang (2014)

Annales Polonici Mathematici

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Let $A_{ζ} = Ω - \bar{ρ (ζ) \cdot Ω}$ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel $K_{ζ} (z)$ of $A_{ζ}$ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that $A_{ζ}$ is non-pseudoconvex when the dimension of $A_{ζ}$ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for $\partial ² l o g K_{ζ} / \partial ζ \partial ζ ̅$ , as well as its boundary behavior.

On n-circled $ℋ^{\infty}$ -domains of holomorphy

Marek Jarnicki, Peter Pflug (1997)

Annales Polonici Mathematici

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We present various characterizations of n-circled domains of holomorphy $G \subset ℂ^{n}$ with respect to some subspaces of $ℋ^{\infty} (G)$ .

The $L^{2}$ $\bar{\partial}$ -Cauchy problem on weakly $q$ -pseudoconvex domains in Stein manifolds

Sayed Saber (2015)

Czechoslovak Mathematical Journal

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Let $X$ be a Stein manifold of complex dimension $n \geq 2$ and $Ω ⋐ X$ be a relatively compact domain with $C^{2}$ smooth boundary in $X$ . Assume that $Ω$ is a weakly $q$ -pseudoconvex domain in $X$ . The purpose of this paper is to establish sufficient conditions for the closed range of $\bar{\partial}$ on $Ω$ . Moreover, we study the $\bar{\partial}$ -problem on $Ω$ . Specifically, we use the modified weight function method to study the weighted $\bar{\partial}$ -problem with exact support in $Ω$ . Our method relies on the $L^{2}$ -estimates by Hörmander (1965) and by Kohn (1973). ...

Global boundary regularity for the $\bar{p a r t i a l}$ -equation on $q$ -pseudo-convex domains

Heungju Ahn (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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For a bounded domain $D$ of $C^{n}$ , we introduce a notion of « $q$ -pseudoconvexity» of new type and prove that for a given $\bar{\partial}$ -closed $(p, r)$ -form $f$ that is smooth up to the boundary on $D$ , and for $r \geq q$ , there exists a $(p, r - 1)$ -form $u$ smooth up to the boundary on $D$ which is a solution of the equation $\bar{\partial} u = f$

A note on locally convex spaces with a basic sequence of $β$ -disks

B. Mirković (1970)

Matematički Vesnik

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Non-embeddable $1$ -convex manifolds

Jan Stevens (2014)

Annales de l’institut Fourier

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We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable $1$ -convex manifold. We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type $(1, - 3)$ . To this end we study small resolutions of $c D_{4}$ -singularities.

A domain whose envelope of holomorphy is not a domain

Edgar Lee Stout (2006)

Annales Polonici Mathematici

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We construct a domain of holomorphy in $ℂ^{N}$ , N≥ 2, whose envelope of holomorphy is not diffeomorphic to a domain in $ℂ^{N}$ .

Free locally convex spaces and $L$ -retracts

Rodrigo Hidalgo Linares, Oleg Okunev (2023)

Commentationes Mathematicae Universitatis Carolinae

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We study the relation of $L$ -equivalence defined between Tychonoff spaces, that is, we study the topological isomorphisms of their respective free locally convex spaces. We introduce the concept of an $L$ -retract in a Tychonoff space in terms of the existence of a special kind of simultaneous extensions of continuous functions, explore the relation of this concept with the Dugundji extension theorem, and find some conditions that allow us to identify $L$ -retracts in various classes of topological...

A note on the commutator of two operators on a locally convex space

Edvard Kramar (2016)

Commentationes Mathematicae Universitatis Carolinae

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Denote by $C$ the commutator $A B - B A$ of two bounded operators $A$ and $B$ acting on a locally convex topological vector space. If $A C - C A = 0$ , we show that $C$ is a quasinilpotent operator and we prove that if $A C - C A$ is a compact operator, then $C$ is a Riesz operator.