On the automorphism groups of convex . . .

We establish that every bounded convex domain in Cn 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 Teichmüller domain of a Riemann surface of genus g> 1 can be holomorphically im-bedded as a convex domain in C3g3