University of Oslo
Professor Løw is mainly interested in holomorphic functions and mappings in higher dimensional complex space and their relation to geometric properties of source and target. His early work consists of direct constructions of functions (such as peak functions and inner functions) and embeddings. In recent years he has been using and developing the Andersen-Lempert theory to handle more sophis-ticated problems. This theory has had a strong influence on multidimensional complex analysis with applications ranging from the homotopy principle in complex analysis to embeddings and solving various more function theoretic problems. Løw has published papers on approximation of diffeomor-phism of totally real submanifolds by automorphisms, stability of polynomial convexity, embeddings of Riemann surfaces with interpolation and completion of symplectic jets, in collaboration with CAS participants Forstneric, Kutzschebauch, Peters and Wold. Successful application of these methods rely on detailed knowledge of the automorphism group of complex manifolds. Løw is now interested in understanding more about the automorphism group of C_× C_ and embeddings into domains of simple geometry. There are also remaining problems on symplectic completions, for instance minimizing the degree and understanding problems on the algebraic aspects of the problem, which can potentially have applications in accelerator physics. He is also interested in the problem of characterizing basins of attraction of holomorphic maps.