{"id":{"repo_id":"trento","oai_identifier":"oai:iris.unitn.it:11572/369312"},"canonical_url":"https://search.dev.ndltd.org/etd/trento/oai:iris.unitn.it:11572/369312","repository":{"repo_id":"trento","name":"Università degli Studi di Trento","base_url":"https://iris.unitn.it/oai/request"},"display":{"title":"Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot groups","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Di Donato, Daniela"],"institution":"Università degli studi di Trento","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T05:04:28Z","subjects":["Settore MAT/05 - Analisi Matematica"],"languages":["eng"],"rights":["info:eu-repo/semantics/closedAccess","license:Tutti i diritti riservati (All rights reserved)"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://dx.doi.org/10.15168/11572_369312","10.15168/11572_369312"],"render_values":[{"text":"http://dx.doi.org/10.15168/11572_369312","href":"http://dx.doi.org/10.15168/11572_369312","code":true},{"text":"10.15168/11572_369312","href":"https://doi.org/10.15168/11572_369312","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/11572/369312","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Di Donato, Daniela"]},{"key":"dc:creator","label":"Author","values":["Di Donato, Daniela"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017"]},{"key":"dc:publisher","label":"Institution","values":["Università degli studi di Trento","place:TRENTO"]},{"key":"dc:relation","label":"Dc Relation","values":["firstpage:1","lastpage:150","numberofpages:150"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Settore MAT/05 - Analisi Matematica"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/closedAccess","license:Tutti i diritti riservati (All rights reserved)"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/11572/369312","http://dx.doi.org/10.15168/11572_369312","10.15168/11572_369312"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:title","label":"Title","values":["Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot groups"]}]}],"canonical_facts":{"dc:contributor":["Di Donato, Daniela"],"dc:creator":["Di Donato, Daniela"],"dc:date":["2017"],"dc:description":["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."],"dc:identifier":["https://hdl.handle.net/11572/369312","http://dx.doi.org/10.15168/11572_369312","10.15168/11572_369312"],"dc:language":["eng"],"dc:publisher":["Università degli studi di Trento","place:TRENTO"],"dc:relation":["firstpage:1","lastpage:150","numberofpages:150"],"dc:rights":["info:eu-repo/semantics/closedAccess","license:Tutti i diritti riservati (All rights reserved)"],"dc:subject":["Settore MAT/05 - Analisi Matematica"],"dc:title":["Intrinsic Differentiability and Intrinsic Regular Surfaces in Carnot groups"],"dc:type":["info:eu-repo/semantics/doctoralThesis"]},"updated_at":"2026-07-24T05:04:28Z"}