On extremal holomorphically contractible families

On behaviour of holomorphically contractible systems under non-monotonic sequences of sets

The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carathéodory pseudodistances, as well as Lempert and Green functions with respect to sequences of domains converging in Hausdorff metric are delivered.

Extremal discs and the holomorphic extension from convex hypersurfaces

Let D be a convex domain with smooth boundary in complex space and let f be a continuous function on the boundary of D. Suppose that f holomorphically extends to the extremal discs tangent to a convex subdomain of D. We prove that f holomorphically extends to D. The result partially answers a conjecture by Globevnik and Stout of 1991.

可双亚纯收缩的全纯 Lagrangian 子流形的标准形式

Normal form of bimeromorphically contractible holomorphic Lagrangian submanifolds

本文通过到法锥的形变研究可双亚纯收缩至一点的紧全纯 Lagrangian 子流形，证明其必为 $CP^n$，且局部辛双全纯等价于余切丛零截面邻域，建立 Weinstein 定理的全纯版本。