On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures

D. Barilari; Y. Chitour; F. Jean; D. Prandi; M. Sigalotti

doi:10.1016/j.matpur.2019.04.008

On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures

D. Barilari
, Y. Chitour
, F. Jean
, D. Prandi
, M. Sigalotti

Laboratoire de Probabilités et Modèles Aléatoires
Université Paris-Saclay
Sorbonne Université

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the C¹ regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C¹.

Original language	English
Pages (from-to)	118-138
Number of pages	21
Journal	Journal des Mathematiques Pures et Appliquees
Volume	133
DOIs	https://doi.org/10.1016/j.matpur.2019.04.008
Publication status	Published - 1 Jan 2020
Externally published	Yes

Keywords

Abnormal extremals
Geodesics
Sub-Riemannian geometry

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10.1016/j.matpur.2019.04.008

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title = "On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures",

abstract = "We prove the C1 regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C1.",

keywords = "Abnormal extremals, Geodesics, Sub-Riemannian geometry",

author = "D. Barilari and Y. Chitour and F. Jean and D. Prandi and M. Sigalotti",

note = "Publisher Copyright: {\textcopyright} 2019",

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doi = "10.1016/j.matpur.2019.04.008",

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AU - Barilari, D.

AU - Chitour, Y.

AU - Jean, F.

AU - Prandi, D.

AU - Sigalotti, M.

PY - 2020/1/1

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N2 - We prove the C1 regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C1.

AB - We prove the C1 regularity for a class of abnormal length-minimizers in rank 2 sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank 2 sub-Riemannian structures of step up to 4 are of class C1.

KW - Abnormal extremals

KW - Geodesics

KW - Sub-Riemannian geometry

U2 - 10.1016/j.matpur.2019.04.008

DO - 10.1016/j.matpur.2019.04.008

M3 - Article

AN - SCOPUS:85063962274

SN - 0021-7824

VL - 133

SP - 118

EP - 138

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

On the regularity of abnormal minimizers for rank 2 sub-Riemannian structures

Abstract

Keywords

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