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 $\mu$ with $\mu (X)=\infty$…