Displaying similar documents to “Local vs. global hyperconvexity, tautness or k -completeness for unbounded open sets in 𝒞 n ”

The Carathéodory topology for multiply connected domains II

Mark Comerford (2014)

Open Mathematics

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We continue our exposition concerning the Carathéodory topology for multiply connected domains which we began in [Comerford M., The Carathéodory topology for multiply connected domains I, Cent. Eur. J. Math., 2013, 11(2), 322–340] by introducing the notion of boundedness for a family of pointed domains of the same connectivity. The limit of a convergent sequence of n-connected domains which is bounded in this sense is again n-connected and will satisfy the same bounds. We prove a result...

Localizations of partial differential operators and surjectivity on real analytic functions

Michael Langenbruch (2000)

Studia Mathematica

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Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set Ω ⊂ ℝ n . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization P m , Θ of the principal part P m is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for P m , Θ . Under additional assumptions P m must be locally hyperbolic. ...

Peak functions on convex domains

Kolář, Martin

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Let Ω ⊂ ℂ n be a domain with smooth boundary and p ∈ ∂ Ω . A holomorphic function f on Ω is called a C k ( k = 0 , 1 , 2 , ⋯ ) peak function at p if f ∈ C k ( Ω ¯ ) , f ( p ) = 1 , and | f ( q ) | < 1 for all q ∈ Ω ¯ ∖ { p } . If Ω is strongly pseudoconvex, then C ∞ peak functions exist. On the other hand, J. E. Fornaess constructed an example in ℂ 2 to show that this result fails, even for C 1 functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function...

Tautness of locally taut domains in complex spaces

Do Duc Thai, Pham Nguyen Thu Trang (2004)

Annales Polonici Mathematici

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A necessary and sufficient condition for tautness of locally taut domains in a weakly Brody hyperbolic complex space is given. Moreover, some results of Kobayashi and Gaussier are deduced as corollaries.

Levi-flat filling of real two-spheres in symplectic manifolds (II)

Hervé Gaussier, Alexandre Sukhov (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

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We consider a compact almost complex manifold ( M , J , ω ) with smooth Levi convex boundary ∂ M and a symplectic tame form ω . Suppose that S 2 is a real two-sphere, containing complex elliptic and hyperbolic points and generically embedded into ∂ M . We prove a result on filling S 2 by holomorphic discs.