# Parametric Jet interpolation for Stein manifolds with the Density Property

## TL;DR

This paper demonstrates that Stein manifolds with the density property can holomorphically interpolate automorphisms with prescribed derivatives at finite points, under certain topological conditions, highlighting their holomorphic flexibility.

## Contribution

It establishes an Oka property for Stein manifolds with the density property, allowing prescribed derivative interpolation for automorphisms depending holomorphically on parameters.

## Key findings

- Interpolation of automorphisms with prescribed derivatives is possible under topological conditions.
- The result links the density property to holomorphic flexibility.
- It advances understanding of the automorphism groups of Stein manifolds.

## Abstract

Given a Stein manifold with the density property, we show that under a suitable topological condition it is possible to prescribe derivatives at a finite number of points to automorphisms depending holomorphically on a Stein parameter. This is an Oka property of the manifold and is related to its holomorphic flexibility.