The Alexander Phenomenon

Dr. Jaikrishnan Janardhanan
Wed, 30th Sep, 2020 4:00 pmAdd to Calendar 2020-09-30 16:00:30 2020-09-30 16:00:30 Title Description Location IIT Palakkad UTC public
Wed, 30th Sep, 2020 6:00 pm

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. I shall then talk about an extension of Alexander's Theorem to a certain class of balanced, finite type domains. I shall also highlight how the use of dynamics in the proof offers some insight on the aforementioned conjecture.

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