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C k -estimates for the ¯ -equation on concave domains of finite type

William Alexandre (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

C k estimates for convex domains of finite type in n are known from [7] for k = 0 and from [2] for k > 0 . We want to show the same result for concave domains of finite type. As in the case of strictly pseudoconvex domain, we fit the method used in the convex case to the concave one by switching z and ζ in the integral kernel of the operator used in the convex case. However the kernel will not have the same behavior on the boundary as in the Diederich-Fischer-Fornæss-Alexandre work. To overcome this problem...

Jensen measures and unbounded B - regular domains in C n

Quang Dieu Nguyen, Dau Hoang Hung (2008)

Annales de l’institut Fourier

Following Sibony, we say that a bounded domain Ω in C n is B -regular if every continuous real valued function on the boundary of Ω can be extended continuously to a plurisubharmonic function on Ω . The aim of this paper is to study an analogue of this concept in the category of unbounded domains in C n . The use of Jensen measures relative to classes of plurisubharmonic functions plays a key role in our work

Local Peak Sets in Weakly Pseudoconvex Boundaries in n

Borhen Halouani (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

We give a sufficient condition for a C ω (resp. C )-totally real, complex-tangential, ( n - 1 ) -dimensional submanifold in a weakly pseudoconvex boundary of class C ω (resp. C ) to be a local peak set for the class 𝒪 (resp. A ). Moreover, we give a consequence of it for Catlin’s multitype.

Quantitative estimates for the Green function and an application to the Bergman metric

Klas Diederich, Gregor Herbort (2000)

Annales de l'institut Fourier

Let D n be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by G D ( . , . ) . In this article we give for a compact subset K D a quantitative upper bound for the supremum sup z K | G D ( z , w ) | in terms of the boundary distance of K and w . This enables us to prove that, on a smooth bounded regular domain D (in the sense of Diederich-Fornaess), the Bergman differential metric B D ( w ; X ) tends to infinity, for X n / { O } , when w D tends to a boundary point....

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