Calculus of Variations and Geometric Measure Theory

Uniform intrinsic differentiability and regular surfaces in Carnot groups

Daniela Di Donato (Università Politecnica della Marche - Ancona)

created by gelli on 28 Oct 2019

12 nov 2019 -- 16:00   [open in google calendar]

Sala Seminari Dipartimento di Matematica di Pisa


The intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces. As in Euclidean spaces, intrinsic regular surfaces can be locally defined in different ways: e.g. as non critical level sets of C1 functions or, equivalently, as graphs of C1 maps between complementary linear subspaces. In Carnot groups the equivalence of these natural definitions is not true any more. The main aim of my research is to find the additional assumptions in order that these notions are equivalent in Carnot groups. More precisely, I characterize intrinsic regular surfaces in terms of suitable weak solutions of non linear first order PDEs. In the context of Heisenberg groups, there are many papers by Serra Cassano and al. about this problem. My research objective is to generalize some of them proved in Heisenberg groups to a more general class of Carnot groups.