Proper Holomorphic Mappings from Domains with Real Analytic Boundary

1984 ◽  
Vol 106 (3) ◽  
pp. 745 ◽  
Author(s):  
Eric Bedford
Keyword(s):  
Holomorphic Mappings ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Proper Holomorphic Mappings

On the Vector Sum of Two Convex Sets in Space

1991 ◽  
Vol 43 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Steven G. Krantz ◽  
Harold R. Parks
Keyword(s):  
Convex Sets ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Vector Sum ◽  
Bounded Convex

In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

scholarly journals On proper holomorphic mappings from domains with T-action

1999 ◽  
Vol 154 ◽  
pp. 57-72 ◽  
Author(s):  
Bernard Coupet ◽  
Yifei Pan ◽  
Alexandre Sukhov
Keyword(s):  
Unit Circle ◽  
Finite Type ◽  
Holomorphic Mapping ◽  
Circular Domain ◽  
Holomorphic Mappings ◽  
Pseudoconvex Domains ◽  
Branch Locus ◽  
Proper Holomorphic Mapping ◽  
Proper Holomorphic Mappings

AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

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