45 research outputs found
Asymptotics of Invariant Metrics in the normal direction and a new characterisation of the unit disk
We give improvements of estimates of invariant metrics in the normal
direction on strictly pseudoconvex domains. Specifically we will give the
second term in the expansion of the metrics. This depends on an improved
localisation result and estimates in the one variable case. Finally we will
give a new characterisation of the unit disk in in terms of the
asymptotic behaviour of quotients of invariant metrics
Embeddings of infinitely connected planar domains into C^2
We prove that every circled domain in the Riemann sphere admits a proper
holomorphic embedding to C^2. Our methods also apply to circled domains with
punctures, provided that all but finitely many of the punctures belong to the
closure of the set of complementary discs.Comment: Analysis and PDE, to appea
Approximation of Partially Smooth Functions
In this paper we discuss approximation of partially smooth functions. The
problem arises naturally in the study of laminated currents
Free dense subgroups of holomorphic automorphisms
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.Comment: 9 page