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math.MG2024
On Carrasco Piaggio's theorem connecting combinatorial modulus and Ahlfors regular conformal dimension
Behnam Esmayli, Ryan Schardine, Nageswari Shanmugalingam
The goal of this paper is to provide an expository description of a result of Carrasco Piaggio connecting the Ahlfors regular conformal dimension of a compact uniformly perfect dou…
math.MG2024
On homogeneous Newton-Sobolev spaces of functions in metric measure spaces of uniformly locally controlled geometry
Ryan Gibara, Ilmari Kangasniemi, Nageswari Shanmugalingam
We study the large-scale behavior of Newton-Sobolev functions on complete, connected, proper, separable metric measure spaces equipped with a Borel measure with …