In this paper, we study the
properties of exhaustion maps defined on Thullen domains and piecewise smooth
intersection domains. In general, “exhaustion between two bounded domains” is a
much weaker condition than biholomorphism, but in the above two cases, we are able
to show that the two concepts are almost the same. In particular, we generalize
Pinchuk’s theorems to the case of exhaustion maps in the domains mentioned
above.