On the automorphism groups of convex domains in C-n

Abstract

We establish that every bounded convex domain in C-n with an automorphism orbit accumulation at a boundary point at which the domain has a sphere contact from inside admits a non-compact 1-parameter subgroup of automorphisms. Notice that this in particular implies that no Teichmuller domain of a Riemann surface of genus g > 1 can be holomorphically imbedded as a convex domain in C3g-3.