2017/09/28 by Gaussier, Hervé, Xianghong Gong, Gong, Xianghong
Mathematics · #30C20 #32H40 #32T15 #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1709.09947
openalex publication_date 2017/09/28 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
We prove that two smooth families of 2-connected domains in \cc are smoothly equivalent if they are equivalent under a possibly discontinuous family of biholomorphisms. We construct, for m ≥ 3, two smooth families of smoothly bounded m-connected domains in \cc, and for n≥2, two families of strictly pseudoconvex domains in \ccn, that are equivalent under discontinuous families of biholomorphisms but not under any continuous family of biholomorphisms. Finally, we give sufficient conditions for the smooth equivalence of two smooth families of domains.