Kernel convergence and biholomorphic mappings in several complex variables

Kernel Convergence and Biholomorphic Mappings in Several Complex Variables

We deal with kernel convergence of domains in Cn which are biholomorphically equivalent to the unit ball B. We also prove that there is an equivalence between the convergence on compact sets of biholomorphic mappings on B, which satisfy a growth theorem, and the kernel convergence. Moreover, we obtain certain consequences of this equivalence in the study of Loewner chains and of starlike and co...

Complex Dynamics in Several Variables

1. Motivation 117 2. Iteration of Maps 118 3. Regular Versus Chaotic Behavior 119 4. The Horseshoe Map and Symbolic Dynamics 120 5. Hénon Maps 123 6. Properties of Horseshoe and Hénon Maps 126 7. Dynamically Defined Measures 127 8. Potential Theory 129 9. Potential Theory in One-Variable Dynamics 131 10. Potential Theory and Dynamics in Two Variables 133 11. Currents and Applications to Dynamic...

Extension and Convergence Theorems for Families of Normal Maps in Several Complex Variables

Let H(X, Y ) ( C(X, Y ) ) represent the family of holomorphic (continuous) maps from a complex (topological) space X to a complex (topological) space Y , and let Y + = Y ∪{∞} be the Alexandroff one–point compactification of Y if Y is not compact, Y + = Y if Y is compact. We say that F ⊂ H(X, Y ) is uniformly normal if {f ◦ φ : f ∈ F , φ ∈ H(M,X)} is relatively compact in C(M,Y +) (with the comp...

Several Complex Variables and Analytic Spaces

D’Angelo, John P. Inequalities from complex analysis. (English summary) 2003e:32001 Fritzsche, Klaus (with Grauert, Hans) From holomorphic functions to complex manifolds. (English summary) 2003g:32001 Grauert, Hans see Fritzsche, Klaus, 2003g:32001 (Nakamura, Shu Gilbert) see Ohsawa, Takeo, 2003d:32001 Ohsawa, Takeo Analysis of several complex variables. (English summary) 2003d:32001 Range, R. ...

Composition Operators and Several Complex Variables