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Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions

Thomas Patrick Pawlaschyk (2016)

Annales Polonici Mathematici

We introduce the notion of the Shilov boundary for some subfamilies of upper semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of that subclass attain their maximum. For certain subfamilies with simple structure we show the existence and uniqueness of the Shilov boundary. We provide its relation to the set of peak points and establish Bishop-type theorems. As an application we obtain a generalization of...

Boundary asymptotics of the relative Bergman kernel metric for hyperelliptic curves

Robert Xin Dong (2017)

Complex Manifolds

We survey variations of the Bergman kernel and their asymptotic behaviors at degeneration. For a Legendre family of elliptic curves, the curvature form of the relative Bergman kernel metric is equal to the Poincaré metric on ℂ 0,1. The cases of other elliptic curves are either the same or trivial. Two proofs depending on elliptic functions’ special properties and Abelian differentials’ Taylor expansions are discussed, respectively. For a holomorphic family of hyperelliptic nodal or cuspidal curves...

B-regularity of certain domains in ℂⁿ

Nguyen Quang Dieu, Nguyen Thac Dung, Dau Hoang Hung (2005)

Annales Polonici Mathematici

We study the B-regularity of some classes of domains in ℂⁿ. The results include a complete characterization of B-regularity in the class of Reinhardt domains, we also give some sufficient conditions for Hartogs domains to be B-regular. The last result yields sufficient conditions for preservation of B-regularity under holomorphic mappings.

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