A complete complex hypersurface in the ball of CN
成果类型：
Article
署名作者：
Globevnik, Josip
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2015.182.3.4
发表日期：
2015
页码：
1067-1091
关键词：
摘要：
In 1977, P. Yang asked whether there exist complete immersed complex submanifolds phi: M-k -> C-N with bounded image. A positive answer is known for holomorphic curves (k = 1) and partial answers are known for the case when k > 1. The principal result of the present paper is a construction of a holomorphic function on the open unit ball B-N of C-N whose real part is unbounded on every path in B-N of finite length that ends on bB(N). A consequence is the existence of a complete, closed complex hypersurface in B-N. This gives a positive answer to Yang's question in all dimensions k, N, 1 <= k < N, by providing properly embedded complete complex manifolds.