Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot Groups
Differential Geometry
2019-12-16 v2 Metric Geometry
Abstract
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 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 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 some results proved by Ambrosio, Serra Cassano, Vittone valid in Heisenberg groups to the more general setting of Carnot groups.
Cite
@article{arxiv.1811.05457,
title = {Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot Groups},
author = {Daniela Di Donato},
journal= {arXiv preprint arXiv:1811.05457},
year = {2019}
}