Erlend Fornaess Wold

Bordered Riemann surfaces in C2

Abstract We prove that the interior of any compact complex curve with smooth boundary in C 2 admits a proper holomorphic embedding into C 2 . In particular, if D is a bordered Riemann surface whose closure admits a holomorphic embedding into C 2 , then D admits a proper holomorphic embedding into C 2 .

FATOU–BIEBERBACH DOMAINS

We show that for any

EMBEDDING RIEMANN SURFACES PROPERLY INTO ℂ2

m\in\NN\cup\{\infty\}

Embeddings of infinitely connected planar domains into ℂ2

there exist

A long ℂ2 which is not Stein

m

Proper holomorphic embeddings into stein manifolds with the density property

disjoint FB domains whose union is dense in

An Estimate for the Squeezing Function and Estimates of Invariant Metrics

\CC^k

Polynomial convexity and totally real manifolds

. In fact we show that any point not in the union is a boundary point for all the domains. We construct FB domains that contains arbitrary countable collections of subvarieties of

A non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary

\CC^k

Embedding univalent functions in filtering Loewner chains in higher dimension

, and we construct FB domains that intersect elements of countable collections of affine subspaces of