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math.MG2023
Fine properties of metric space-valued mappings of bounded variation in metric measure spaces
Ivan Caamano, Josh Kline, Nageswari Shanmugalingam
Here we consider two notions of mappings of bounded variation (BV) from the metric measure space into the metric space; one based on relaxations of Newton-Sobolev functions, and th…
math.MG2019
Carathéodory-type extension theorem with respect to prime end boundaries
Joshua Kline, Jeff Lindquist, Nageswari Shanmugalingam
We prove a Carathéodory-type extension of BQS homeomorphisms between two domains in proper, locally path-connected metric spaces as homeomorphisms between their prime end closures.…