Embedding complete holomorphic discs through discrete sets

2016/04/03 by Globevnik, Josip
#32C50 #32H02 #32Q40 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00684

Abstract

Let U be the open unit disc in C and let B be the open unit ball in C². We prove that every discrete subset of B is contained in the range f(U) of a complete, proper holomorphic embedding f:U-->B. Here the completeness of f means that for any path p:[0,1)-->U such that |p(t)|-->1 as t-->1, the path t--> f(p(t)) from [0,1) to B has infinite length.

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