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.

Finiteness theorems for holomorphic mapping from products of hyperbolic Riemann surfaces

2017 ◽  
Vol 28 (07) ◽  
pp. 1750060
Author(s):  
Divakaran Divakaran ◽  
Jaikrishnan Janardhanan
Keyword(s):  
Finite Type ◽  
Bounded Domain ◽  
Riemann Surfaces ◽  
Holomorphic Mapping ◽  
Hyperbolic Manifolds ◽  
Holomorphic Mappings ◽  
Finite Set ◽  
Finiteness Theorems ◽  
Hyperbolic Riemann Surfaces

We prove that the space of dominant/non-constant holomorphic mappings from a product of hyperbolic Riemann surfaces of finite type into certain hyperbolic manifolds that can be covered by a bounded domain is a finite set.

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