W-volume for planar domains with circular boundary
Franco Vargas Pallete
Arizona State University
School of Mathematical and Statistical Sciences
In this talk I'll discuss how to extend the notion of Epstein maps for submanifolds in the conformal boundary of hyperbolic space. That construction will be used to define W-volume for region with circular boundary. I'll discuss then how to use that definition to bound renormalized volume for classical Schottky groups, as well as to give a geometric interpretation for the Loewner energy for sufficiently regular Jordan curves. This is based on join work with Jeff Brock.
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