Extension problems for biholomorphisms in several complex variables

Zhenjun Hu, Purdue University

Abstract

One of the basic problems in several complex variables is that whether weakly pseudoconvex domains and strongly pseudoconvex domains can be biholomorphic to each other. It is proved in this thesis that if $\Omega\sb1$ and $\Omega\sb2$ are bounded domains in $\doubc\sp{n}$ and $\Omega\sb1$ is weakly (not strongly) pseudoconvex domain with boundary smoothness greater than $16n+15$ and $\Omega\sb2$ is strongly pseudoconvex domain with boundary smoothness greater than $6n+8,$ then $\Omega\sb1$ and $\Omega\sb2$ are not biholomorphic to each other. This is the corollary of the main theorem of this thesis which states that the biholomorphism between $\Omega\sb1$ and $\Omega\sb2$ above can extend to a $C\sp1$ map from $\bar\Omega\sb1$ to $\bar\Omega\sb2.$

Degree

Ph.D.

Advisors

Bell, Purdue University.

Subject Area

Mathematics

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