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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