Uniform intrinsic differentiability and regular surfaces in Carnot groups

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Daniela di Donato
Universita' di Trento
Abstract. The intrinsic regular surfaces in Carnot groups play the same role as C^1 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 C^1 functions or, equivalently, as graphs of C^1 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.