oai:scholarship.rice.edu:1911/13330

# On proper holomorphic mappings: Smooth extension to the boundary

## Abstract

The subject of proper holomorphic mapping is currently a very active area of research. One of the most interesting questions is the following: if \Omega\sb1, \Omega\sb2 \subseteq C\sp{n} are open sets with C\sp{\infty} boundaries and if F : \Omega\sb1 \to \Omega\sb2 is a biholomorphic map, is it true that F extends to a C\sp{\infty} function on {\bar \Omega\sb1}? In my thesis, the conclusion of S. Bell, D. Catlin, K. Diederid and J. E. Formnass (1981, 1982) had been improved. Under certain assumptions about the smoothness of the Bergman kernel Function on the boundary of domain, some new conclusions of proper holomorphic mapping smooth extension to the boundary are also obtained