Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot Groups

摘要

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as DOUBLE-STRUCK CAPITAL 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 or as continuously intrinsic differentiable graphs. The equivalence of these natural definitions is the problem that we are studying. Precisely our aim is to generalize the results on Ambrosio et al. (J. Geom. Anal., 16, 187-232, 2006) valid in Heisenberg groups to the more general setting of Carnot groups.