Affine Subspaces of Curvature Functions from Closed Planar Curves

Given a pair of real functions (k, f), we study the conditions they must satisfy for [Formula: see text] to be the curvature in the arc-length of a closed planar curve for all real [Formula: see text] . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential...

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Autor principal: Alese, Leonardo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550244/
https://www.ncbi.nlm.nih.gov/pubmed/34720692
http://dx.doi.org/10.1007/s00025-021-01378-6
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author Alese, Leonardo
author_facet Alese, Leonardo
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description Given a pair of real functions (k, f), we study the conditions they must satisfy for [Formula: see text] to be the curvature in the arc-length of a closed planar curve for all real [Formula: see text] . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied.
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spelling pubmed-85502442021-10-29 Affine Subspaces of Curvature Functions from Closed Planar Curves Alese, Leonardo Results Math Article Given a pair of real functions (k, f), we study the conditions they must satisfy for [Formula: see text] to be the curvature in the arc-length of a closed planar curve for all real [Formula: see text] . Several equivalent conditions are pointed out, certain periodic behaviours are shown as essential and a family of such pairs is explicitely constructed. The discrete counterpart of the problem is also studied. Springer International Publishing 2021-03-20 2021 /pmc/articles/PMC8550244/ /pubmed/34720692 http://dx.doi.org/10.1007/s00025-021-01378-6 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis 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
Alese, Leonardo
Affine Subspaces of Curvature Functions from Closed Planar Curves
title Affine Subspaces of Curvature Functions from Closed Planar Curves
title_full Affine Subspaces of Curvature Functions from Closed Planar Curves
title_fullStr Affine Subspaces of Curvature Functions from Closed Planar Curves
title_full_unstemmed Affine Subspaces of Curvature Functions from Closed Planar Curves
title_short Affine Subspaces of Curvature Functions from Closed Planar Curves
title_sort affine subspaces of curvature functions from closed planar curves
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550244/
https://www.ncbi.nlm.nih.gov/pubmed/34720692
http://dx.doi.org/10.1007/s00025-021-01378-6
work_keys_str_mv AT aleseleonardo affinesubspacesofcurvaturefunctionsfromclosedplanarcurves

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