Carathéodory Balls and Proper Holomorphic Maps on Multiply-Connected Planar Domains

Explore the intricacies of Carathéodory balls and proper holomorphic maps on multiply-connected planar domains in this 49-minute lecture by Patrick Ng from the University of Hong Kong. Delivered as part of the Focus Program on Analytic Function Spaces and their Applications at the Fields Institute on October 28th, 2021, delve into key concepts such as open problems, natural questions, and proper holomorphic maps. Examine circular domains, circularly sped domains, and proper maps through illustrative examples. Investigate the Shocky double, infinite product, and Supima Omega R, gaining a deeper understanding of these complex mathematical concepts and their applications in analytic function spaces.

Introduction
Open problem
Natural question
Proper holomorphic maps
Circular domains
Circularlyspeed domains
Proper maps
Example
Shocky double
Infinite product
Supima
Omega R