Abstract Let ? be a proper open cone in real Banach space V . We show that the tube domain V ? i ? ? {V\oplus i\Omega} over is biholomorphic to bounded symmetric if and only normal linearly homogeneous Finsler cone, which equiva...

In this article, we study the higher-order regularity of Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. By developing sharp new parabolic Schauder estimates cylinders, proved that when generic fibers Iitaka fibration are biholomorphic to each other, converges in C loc ? -topology away from singular a negative Kähler-Einstein metric base manifold. particular...

Let (M, g) be a simply connected complete Kähler manifold with nonpositive sectional curvature. Assume that g has constant negative holomorphic sectional curvature outside a compact set. We prove that M is then biholomorphic to the unit ball in Cn, where dimCM = n. Résumé. Soit (M, g) une variété kählérienne complète et simplement connexe à courbure sectionnelle non-positive. Supposons que g ai...

The Chern-Moser normal form and its analog on finite type hypersurfaces in general do not respect symmetries. Extending the work of N. K. Stanton, we consider the local equivalence problem for symmetric Levi degenerate hypersurfaces of finite type in C2. The results give complete normalizations for such hypersurfaces, which respect the symmetries. In particular, they apply to tubes and rigid hy...

Let (M, g) be a complete non compact Kähler manifold with non-negative and bounded holomorphic bisectional curvature. Extending our techniques developed in [8], we prove that the universal cover M̃ of M is biholomorphic to Cn provided either that (M, g) has average quadratic curvature decay, or M supports an eternal solution to the Kähler-Ricci flow with non-negative and uniformly bounded holomo...