Proper holomorphic curves attached to domains

Published 8 Nov 2018 in math.CV | (1811.03363v1)

Abstract: Let D be a domain in Cⁿ with smooth boundary, of finite 1-type at a point p in the boundary and such that the closure of D has a basis of Stein Runge neighborhoods. Assume that there exists an analytic disc which intersects the closure of D exactly at p. We construct proper holomorphic maps from any open Riemann surface S which are attached to the closure of D exactly at p.

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