Metric Currents and Differentiable Structures

[摘要] We investigate Ambrosio and Kirchheim;;s theory of currents in metric measure spaces, assuming the spaces admit generalized differentiation theorems as studied by Cheeger and Keith. In this case, we show that metric currents of absolutely continuous mass can be realized by integration against vector-valued measures. We characterize currents in Carnot groups, provided again that their masses are absolutely continuous with respect to the underlying Haar measure.We also prove an equivalence between two one-sided definitions of quasiconformality for maps between metric measure spaces, using methods motivated by the study of metric currents.

[发布机构] University of Michigan

[效力级别] Mathematics

[关键词] Metric Currents;Mathematics;Science;Mathematics