Characterizations of p-superharmonic functions on metric spaces

Characterizations of Sobolev Inequalities on Metric Spaces

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.

DIFFERENTIABILITY OF p-HARMONIC FUNCTIONS ON METRIC MEASURE SPACES

We study p-harmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a p-Poincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sharp, since there are examples of metric spaces and p-harmonic functions that fail to be locally Lipschitz co...

SUPERHARMONIC functions on foliations

We use techniques from geometric analysis to prove that any positive, leafwise superharmonic, measurable function on a Riemannian measurable foliation with transverse invariant measure, finite total volume and complete leaves is, in fact, constant on a.e. leaf.

Spaces of Lipschitz Functions on Metric Spaces

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.

Characterizations of Compactness for Metric Spaces