Auditorium, Ahalia Campus
A famous result of H. Alexander asserts that any proper holomorphic self-map of the unit (Euclidean) ball in higher dimensions is an automorphism. Alexander's result has been extended to various classes of domains including strictly pseudoconvex domains (by Pinchuk) and weakly pseudoconvex domains with real-analytic boundary (by Bedford and Bell). It is conjectured that any proper holomorphic self-map of a smoothly bounded pseudoconvex domain in higher dimensions must be an automorphism. In this talk, I shall first briefly survey some of the prominent Alexander-type results.
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