Riemann Domains with Boundary of Capacity Zero

Hirotaka Fujimoto
1971 Nagoya mathematical journal  
The well-known Thullen-Remmert-Stein's theorem ([9], [7]) asserts that, for a domainDinCNand ann-dimensional irreducible analytic setSinD, a purely n-dimensional analytic setAinD—Shas an essential singularity at any point in 5 ifAhas at least one essential singularity in S. In [1], E. Bishop generalized this to the case thatAhas the boundary of capacity zero in his sense. Afterwards, in [8], W. Rothstein obtained more precise informations on the essential singularities ofAunder the assumption
more » ... er the assumption dimA= 1. The main purpose in this paper is to generalize these Rothstein's results to the case of arbitrary dimensional analytic sets.
doi:10.1017/s0027763000014501 fatcat:obx4yeskr5cvzeek5pwrjudxu4