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Rigidity And Regularity Of Holomorphic Mappings

Electronic Theses of Indian Institute of Science

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Title Rigidity And Regularity Of Holomorphic Mappings
 
Creator Balakumar, G P
 
Subject Holomorphic Mappings
Mappings (Mathematics)
Hypersurfaces
CR Mappings
Psudoconvex Domains
Automorphisms
Abelian Automorphism
Holomorphic Functions
Model Domains
Kobayashi Metric
Mathematics
 
Description We deal with two themes that are illustrative of the rigidity and regularity of holomorphic
mappings.

The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces which is a well studied subject for it is linked with the problem of studying the boundary behaviour of proper holomorphic mappings between domains bounded by such hypersurfaces. More specifically, we study the regularity of Lipschitz CR mappings from an h-extendible(or semi-regular) hypersurface in Cn .Under various assumptions on the target hypersurface, it is shown that such mappings must be smooth. A rigidity result for proper holomorphic mappings from strongly pseudo convex domains is also proved.
The second theme dealt with, is the classification upto biholomorphic equivalence of model domains with abelian automorphism group in C3 .It is shown that every model domain i.e.,a hyperbolic rigid polynomial domainin C3 of finite type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight.
 
Contributor Verma, Kaushal
 
Date 2015-07-16T07:34:08Z
2015-07-16T07:34:08Z
2015-07-16
2012-07
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2447
http://etd.ncsi.iisc.ernet.in/abstracts/3160/G25447-Abs.pdf
 
Language en_US
 
Relation G25447