Semicontinuity of the Automorphism Groups of Domains with Rough Boundary | Zendy

Steven G. Krantz | Zendy

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Semicontinuity of the Automorphism Groups of Domains with Rough Boundary

Author(s) -

Steven G. Krantz

Publication year - 2012

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2012/934295

Subject(s) - mathematics , automorphism , combinatorics , boundary (topology) , path (computing) , automorphism group , matrix (chemical analysis) , mathematical analysis , composite material , materials science , computer science , programming language

Based on some ideas of Greene and Krantz, we studythe semicontinuity of automorphism groups of domains in oneand several complex variables. We show that semicontinuity failsfor domains in , , with Lipschitz boundary, but it holdsfor domains in with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitzdomains. These include Bergman curvature, stability propertiesfor the Bergman kernel, and also some ideas about equivariantembeddings

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