Geometric Measure Theory in Non Euclidean Spaces

Geometric Measure Theory and, in particular, the theory of currents, is one of the most basic tools in problems in Geometric Analysis, providing a parametric-free description of geometric objects which is very efficient in the study of convergence, analysis of concentration and cancellation effects, chenges of topology, existence of solutions to Plateu's problem, etc. In the last years the PI and collaborators obtained ground-breaking results on the theory of currents in metric spaces and on the theory of surface measures in Carnot-Caratheodory spaces. The goal of the project is a wide range analysis of Geometric Measure Theory in spaces with a non-Euclidean structure, including infinite-dimensional spaces.

Grant Agreement