Conformal Equivalence and Rings of Analytic Functions | Department of Mathematics

Conformal Equivalence and Rings of Analytic Functions

Event Information
Event Location: 
GAB 461
Event Date: 
Friday, April 29, 2016 - 2:00pm

We will present a proof of a theorem of Lipman Bers which states that two open sets in the complex plane are conformally equivalent if and only if their respective sets of analytic functions are isomorphic as rings.

We will also show that, if we assume the rings are endowed with the topology of uniform convergence on compact sets, the ring isomorphism is necessarily a homeomorphism.

We will end by showing that the relation of conformality can be seen as a relation on a standard Borel space where each equivalence class is analytic.