2005/07/27 by Buma L. Fridman, Buma Fridman, Fridman, Buma +2
Mathematics · #32M05 #54H15 #Advanced Differential Equations and Dynamical Systems #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.CV #msc:32M05 #msc:54H15
paper · pdf · doi:10.48550/arxiv.math/0507574
10 pages
arxiv created 2005/07/27 · openalex publication_date 2005/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the fixed point sets of holomorphic self-maps of a bounded domain in \Bbb Cn. Specifically we investigate the least number of fixed points in general position in the domain that forces any automorphism (or endomorphism) to be the identity. We have discovered that in terms of this number one can give the necessary and sufficient condition for the domain to be biholomorphic to the unit ball. Other theorems and examples generalize and complete previous results in this area, especially the recent work of Jean-Pierre Vigué.