Surface measure on, and the local geometry of, sub-Riemannian manifolds

We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of sma...

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Detalles Bibliográficos
Autores principales: Don, Sebastiano, Magnani, Valentino
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10598233/
https://www.ncbi.nlm.nih.gov/pubmed/37886618
http://dx.doi.org/10.1007/s00526-023-02590-8
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author Don, Sebastiano
Magnani, Valentino
author_facet Don, Sebastiano
Magnani, Valentino
author_sort Don, Sebastiano
collection PubMed
description We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of small metric balls.
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spelling pubmed-105982332023-10-26 Surface measure on, and the local geometry of, sub-Riemannian manifolds Don, Sebastiano Magnani, Valentino Calc Var Partial Differ Equ Article We prove an integral formula for the spherical measure of hypersurfaces in equiregular sub-Riemannian manifolds. Among various technical tools, we establish a general criterion for the uniform convergence of parametrized sub-Riemannian distances, and local uniform asymptotics for the diameter of small metric balls. Springer Berlin Heidelberg 2023-10-24 2023 /pmc/articles/PMC10598233/ /pubmed/37886618 http://dx.doi.org/10.1007/s00526-023-02590-8 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Don, Sebastiano
Magnani, Valentino
Surface measure on, and the local geometry of, sub-Riemannian manifolds
title Surface measure on, and the local geometry of, sub-Riemannian manifolds
title_full Surface measure on, and the local geometry of, sub-Riemannian manifolds
title_fullStr Surface measure on, and the local geometry of, sub-Riemannian manifolds
title_full_unstemmed Surface measure on, and the local geometry of, sub-Riemannian manifolds
title_short Surface measure on, and the local geometry of, sub-Riemannian manifolds
title_sort surface measure on, and the local geometry of, sub-riemannian manifolds
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10598233/
https://www.ncbi.nlm.nih.gov/pubmed/37886618
http://dx.doi.org/10.1007/s00526-023-02590-8
work_keys_str_mv AT donsebastiano surfacemeasureonandthelocalgeometryofsubriemannianmanifolds
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