arXiv subjects
Publications and source records attributed to Rafael B. Andrist.
The basin of attraction of a uniformly attracting sequence of holomorphic automorphisms that agree to a certain order in the common fixed point, is biholomorphic to $\mathbb{C}^n$. We also give sufficient estimates how large this order has to be.
All Gizatullin surfaces that admit such a $\mathbb{C}^+$-action for which the quotient is a $\mathbb{C}^1$-fibration with a reduced degenerate fibre, have the density property. We also give a description of the identity component of the group of holomorphic automorphisms of these surfaces.
Gizatullin surfaces of type $[[0,0,-r_2,-r_3]]$ can be described by the equations $yu = x P(x)$, $xv = u Q(u)$ and $yv = P(x) Q(u)$ in $\mathbb{C}^4_{x,y,u,v}$ where $P$ and $Q$ are non-constant polynomials. We establish the algebraic density property for smooth Gizatullin surfaces of this type. Moreover we also prove the density property for smooth surfaces given by these equations when $P$ and $Q$ are holomorphic functions.
We generalize the notion of the density property for complex manifolds to holomorphic fibrations, and introduce the notion of the fibred density property. We prove that the natural fibration of the spectral ball over the symmetrized polydisc enjoys the fibred density property and describe the automorphism group of the spectral ball.
We give necessary and sufficient conditions for solving the spectral Nevanlinna--Pick lifting problem. This reduces the spectral Nevanlinna--Pick problem to a jet interpolation problem into the symmetrized polydisc.
We study ellipticity properties of complements of compact subsets of Stein manifolds.
In this short note we show that $\mathbb C^n\setminus\bar{\mathbb B^n}$ is not subelliptic for $n \geq 3$. This is done by proving a Hartogs type extension theorem for holomorphic vector bundles bundles.
We show the existence of free dense subgroups, generated by 2 elements, in the holomorphic shear and overshear group of complex-Euklidean space and extend this result to the group of holomorphic automorphisms of Stein manifolds with Density Property, provided there exists a generalized translation. The conjugation operator associated to this generalized translation is hypercyclic on the topological space of holomorphic automorphisms.
It is shown that any open Riemann surface can be immersed in any Stein manifold with (volume) density property and of dimension at least 2, if the manifold possesses an exhaustion with holomorphically convex compacts such that their complement is connected. The immersion can be made into an embedding if the dimension is at least 3. As an application, it is shown that Stein manifolds with (volume) density property and of dimension at least 3, are characterized among all other complex manifolds by their semigroup of holomorphic endomorphisms.
We apply Nevanlinna theory for algebraic varieties to Danielewski surfaces and investigate their group of holomorphic automorphisms. Our main result states that the overshear group which is known to be dense in the identity component of the holomorphic automorphism group, is a free amalgamated product.
Finite dimensional Stein spaces admitting a proper holomorphic embedding of the complex line are characterized, among all complex spaces, by their holomorphic endomorphism semigroup in the sense that any semigroup isomorphism induces either a biholomorphic or an antibiholomorphic map between them.