Universal holomorphic maps with slow growth I. An Algorithm

Abstract

We design an Algorithm to fabricate universal holomorphic maps between any two complex Euclidean spaces, within preassigned transcendental growth rate. As by-products, universal holomorphic maps from ${\mathbb{C}}^n$ to ${\mathbb{CP}}^m$ ($n⩽m$) and to complex tori having slow growth are obtained. We take inspiration from Oka manifolds theory, Nevanlinna theory, and hypercyclic operators theory.

arXiv commentfinal version

References in corpus (4)

• Recent developments on Oka manifolds
• Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps
• Gunning-Narasimhan's theorem with a growth condition
• Universal Entire Curves in Projective Spaces with Slow Growth

Cited by in corpus (2)

• Entire curves producing distinct Nevanlinna currents
• Oka-1 manifolds