ncts

This is an ongoing project to study collections of measures that are negligible in a sense of "modules". The idea originated in complex analysis as "a conformal module of a family of curves" in looking for an invariant object under conformal transformations on the complex plane. Later the definition of the module was successfully applied to the nonlinear potential theory and quasiconformal analysis in a wider sense in Euclidean spaces. B. Fuglede, by studying the completion of functional spaces, generalized the notion of the module of a family of curves to the module of a family of measures. A collection of measures is exceptional if the corresponding module vanishes. We aim to find exceptional families of measures on Carnot groups, related to geometric objects such as "intrinsic graphs". It leads to the notion of a Grassmannian on specific Carnot groups. This is a joint work with Bruno Franchi, University of Bologna, Italy.