Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem
A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to bethe natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘nat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-01-01
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| Series: | Analysis and Geometry in Metric Spaces |
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| Online Access: | https://doi.org/10.2478/agms-2014-0010 |
| _version_ | 1818720408678957056 |
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| author | Franchi Bruno Marchi Marco Serapioni Raul Paolo |
| author_facet | Franchi Bruno Marchi Marco Serapioni Raul Paolo |
| author_sort | Franchi Bruno |
| collection | DOAJ |
| description | A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to bethe natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meantto stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensionalintrinsic Lipschitz graphs are sets with locally finite G-perimeter. From this a Rademacher’s typetheorem for one codimensional graphs in a general class of groups is proved. |
| first_indexed | 2024-12-17T20:22:22Z |
| format | Article |
| id | doaj.art-af3a69c325be46a781e057ef2309bb88 |
| institution | Directory Open Access Journal |
| issn | 2299-3274 |
| language | English |
| last_indexed | 2024-12-17T20:22:22Z |
| publishDate | 2014-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Analysis and Geometry in Metric Spaces |
| spelling | doaj.art-af3a69c325be46a781e057ef2309bb882022-12-21T21:33:54ZengDe GruyterAnalysis and Geometry in Metric Spaces2299-32742014-01-012110.2478/agms-2014-0010agms-2014-0010Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheoremFranchi Bruno0Marchi Marco1Serapioni Raul Paolo2Dipartimento di Matematica, Università di Bologna, Piazza di porta San Donato, 5, 40126 Bologna, Italy Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini, 50, 20133 Milano, Italy Dipartimento di Matematica, Università di Trento, Povo, Via Sommarive 14, 38123, Trento, Italy A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra.We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to bethe natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meantto stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensionalintrinsic Lipschitz graphs are sets with locally finite G-perimeter. From this a Rademacher’s typetheorem for one codimensional graphs in a general class of groups is proved.https://doi.org/10.2478/agms-2014-0010carnot groupsrectifiable sets intrinsic lipschitz functions rademacher’s theorem |
| spellingShingle | Franchi Bruno Marchi Marco Serapioni Raul Paolo Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem Analysis and Geometry in Metric Spaces carnot groups rectifiable sets intrinsic lipschitz functions rademacher’s theorem |
| title | Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem |
| title_full | Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem |
| title_fullStr | Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem |
| title_full_unstemmed | Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem |
| title_short | Differentiability and ApproximateDifferentiability for Intrinsic LipschitzFunctions in Carnot Groups and a RademacherTheorem |
| title_sort | differentiability and approximatedifferentiability for intrinsic lipschitzfunctions in carnot groups and a rademachertheorem |
| topic | carnot groups rectifiable sets intrinsic lipschitz functions rademacher’s theorem |
| url | https://doi.org/10.2478/agms-2014-0010 |
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