Event Details
Título: A complete complex hypersurface in the ball of $\mathbb{C}^N$
Impartido por Josip Globevnik, Universidad de Liubliana (Eslovenia)
Impartido por Josip Globevnik, Universidad de Liubliana (Eslovenia)
ABSTRACT: In 1977 P. Yang asked whether there exist complete immersed complex sub- manifolds $\varphi:M^k\to \mathbb{C}^N$ with bounded image. A positive answer is known for holomorphic curves ($k=1$) and partial answers are known in the case when $k>1$. In the talk we will describe how to construct a holomorphic function on the open unit ball $\mathbb{B}_N$ of $\mathbb{C}^N$ , $N\geq 2$, whose real part is unbounded on every path in $\mathbb{B}_N$ of finite length that ends on $b\mathbb{B}_N$. This implies the existence of a complete, closed complex hypersurface in $\mathbb{B}_N$, and gives a positive answer to Yang’s question in all dimensions $k$, $N$, $1\leq k \lt N$, by providing properly embedded complete complex manifolds.
