Calculus of Variations and Geometric Measure Theory
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D. Di Donato

Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot Groups

created by didonato on 15 Nov 2018

[BibTeX]

preprint

Inserted: 15 nov 2018

Year: 2018

ArXiv: 1811.05457 PDF

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 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 some results proved by Ambrosio, Serra Cassano, Vittone valid in Heisenberg groups to the more general setting of Carnot groups.

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