Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot groups

The main object of our research is the notion of "intrinsic regular surfaces" introduced and studied by Franchi, Serapioni, Serra Cassano in a Carnot group G. More precisely, an intrinsic regular hypersurface (i.e. a topological codimension 1 surface) S is a subset of G which is locally defined as a non critical level set of a C^1 intrinsic function. In a similar way, a k-codimensional intrinsic regular surface is locally defined as a non critical level set of a C^1 intrinsic vector function. Through Implicit Function Theorem, S can be locally represented as an intrinsic graph by a function phi. Here the intrinsic graph is defined as follows: let V and W be complementary subgroups of G, then the intrinsic graph of phi defined from W to V is the set { A \cdot phi(A) | A belongs to W}, where \cdot indicates the group operation in G. A fine characterization of intrinsic regular surfaces in Heisenberg groups (examples of Carnot groups) as suitable 1-codimensional intrinsic graphs has been established in [1]. We extend this result in a general Carnot group introducing an appropriate notion of differentiability, denoted uniformly intrinsic differentiability, for maps acting between complementary subgroups of G. Finally we provide a characterization of intrinsic regular surfaces in terms of existence and continuity of suitable "derivatives" of phi introduced by Serra Cassano et al. in the context of Heisenberg groups. All the results have been obtained in collaboration with Serapioni. [1] L.Ambrosio, F. Serra Cassano, D. Vittone, \emph{Intrinsic regular hypersurfaces in Heisenberg groups}, J. Geom. Anal. 16, (2006), 187-232.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2017

Author dc:creator

• Di Donato, Daniela

• Settore MAT/05 - Analisi Matematica

Statement dc:rights

• info:eu-repo/semantics/closedAccess
• license:Tutti i diritti riservati (All rights reserved)

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_369312
10.15168/11572_369312

OAI identifier oai:identifier

oai:iris.unitn.it:11572/369312