The first thirty years of Andersen-Lempert theory

Abstract

In this paper we expose the impact of the fundamental discovery, made by Erik Andersén and László Lempert in 1992, that the group generated by shears is dense in the group of holomorphic automorphisms of complex Euclidean spaces of dimensions $n>1$. In three decades since its publication, their groundbreaking work led to the discovery of several new phenomena and to major new results in complex analysis and geometry involving Stein manifolds and affine algebraic manifolds with many automorphisms. The aim of this survey is to present some focal points of these developments, with a view towards the future.

References in corpus (5)

• Criteria for the density property of complex manifolds
• Bordered Riemann surfaces in C^2
• Oka properties of complements of holomorphically convex sets
• Holomorphic families of Fatou-Bieberbach domains and applications to Oka manifolds
• Manifolds with infinite dimensional group of holomorphic automorphisms and the Linearization Problem

Cited by in corpus (3)

• Recent developments on Oka manifolds
• Oka domains in Euclidean spaces
• Tame sets in homogeneous spaces