We prove a characterization of the domains in en with an automorphism orbit accumulating at a boundary point at which the boundary is real analytic and convex up to a biholomorphic change of local coordinates. This result generalizes the well-known Wong-Rosay theorem on strongly pseudoconvex domains to the case of locally convex domains with real analytic boundaries.

We are interested in classifying all connected complex manifolds M of dimension n ≥ 2 admitting effective actions of the unitary group Un by biholomorphic transformations. One motivation for our study was the following question that we learned from S. Krantz: assume that the group Aut(M) of all biholomorphic automorphisms of M and the group Aut(C) of all biholomorphic automorphisms of C are iso...

Yau’s uniformization conjecture states: a complete noncompact Kähler manifold with positive holomorphic bisectional curvature is biholomorphic to C. The Kähler-Ricci flow has provided a powerful tool in understanding the conjecture, and has been used to verify the conjecture in several important cases. In this article we present a survey of the Kähler-Ricci flow with focus on its application to...

In this paper we prove: if a bounded domain with $C^2$ boundary covers manifold which has finite volume respect to either the Bergman volume, Kähler–Einstein or Kobayashi–Eisenman then is biholomorphic unit ball. This answers question attributed Yau. Further, when convex can assume that only $C^{1,\epsilon}$ regularity.

We study the local equivalence problem for real-analytic (Cω) hypersurfaces M5⊂C3 that, in some holomorphic coordinates (z1,z2,w)∈C3 with w=u+ −1v, are rigid sense that their graphing functions u=F(z1,z2,z‾1,z‾2) independent of v. Specifically, we group Holrigid(M) biholomorphic transformations form (z1,z2,w)⟼(f1(z1,z2),f2(z1,z2),aw+g(z1,z2)), where a∈R∖{0} and D(f1,f2)/D(z1,z2)≠0, which preser...

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space C . We also show that the volume growth condition can be removed if ...