We introduce new biholomorphic invariants for real-analytic hypersurfaces in C and show how they can be used to show that a hypersurface possesses few automorphisms. We give conditions, in terms of the new invariants, guaranteeing that the stability group is finite, and give (sharp) bounds on the cardinality of the stability group in this case. We also give a sufficient condition for the stabil...

Any (global) deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

Abstract. Given a family of biholomorphisms φt on a noncompact complex manifold M , we provide conditions, on φt, under which M is biholomorphic to C. As an application, we generalize previous results in [1]. We prove that if (M, g) is a complete non-compact gradient Kähler-Ricci soliton with potential function f which is either steady with positive Ricci curvature so that the scalar curvature ...

We construct families of convex domains that are biholomorphic to bounded domains, but not domains. This is accomplished by finding an obstruction related the Gromov hyperbolicity Kobayashi metric.