On the extension of complex structures on compact pseudoconvex complex manifolds

Sanghyun Cho, Purdue University

Abstract

We prove the extension of complex structures on compact pseudoconvex complex manifolds of finite 1-type. Let $\overline{M}$ be a weakly pseudoconvex compact complex manifold of finite 1-type with smooth boundary. Then we show that $\overline{M}$ can be holomorphically embedded into a larger strongly pseudoconvex compact complex manifold $\Omega$. Also we show that $\overline{M}$ can be holomorphically embedded into a Stein manifold if $M$ is a Stein manifold. To show these embedding theorems, we prove a bumping theorem in domains of finite type in $\doubc\sp n$ and prove stability theorem for holomorphic embeddings.

Degree

Ph.D.

Advisors

Catlin, Purdue University.

Subject Area

Mathematics

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