Affine Subspaces of Curvature Functions from Closed Planar Curves

Leonardo Alese

doi:10.1007/s00025-021-01378-6

Affine Subspaces of Curvature Functions from Closed Planar Curves

Leonardo Alese

Institute of Geometry (5070)

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

Abstract

Given a pair of real functions (k, f), we study the conditions they must satisfy for k+ λf to be the curvature in the arc-length of a closed planar curve for all real λ. 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.

Original language	English
Article number	70
Number of pages	14
Journal	Results in mathematics
Volume	76
Issue number	2
DOIs	https://doi.org/10.1007/s00025-021-01378-6
Publication status	Published - May 2021

Keywords

Closed curves
interpolation of curvature

ASJC Scopus subject areas

Applied Mathematics
Mathematics (miscellaneous)

Fields of Expertise

Information, Communication & Computing

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10.1007/s00025-021-01378-6Licence: CC BY 4.0

Cite this

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title = "Affine Subspaces of Curvature Functions from Closed Planar Curves",

abstract = "Given a pair of real functions (k, f), we study the conditions they must satisfy for k+ λf to be the curvature in the arc-length of a closed planar curve for all real λ. 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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Affine Subspaces of Curvature Functions from Closed Planar Curves

Abstract

Keywords

ASJC Scopus subject areas

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