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Isoperimetric equalities for rosettes

Differential Geometry 2020-05-12 v1

Abstract

In this paper we study the isoperimetric-type equalities for rosettes, i.e. regular closed planar curves with non-vanishing curvature. We find the exact relations between the length and the oriented area of rosettes based on the oriented areas of the Wigner caustic, the Constant Width Measure Set and the Spherical Measure Set. We also study and find new results about the geometry of affine equidistants of rosettes and of the union of rosettes.

Keywords

Cite

@article{arxiv.1605.08304,
  title  = {Isoperimetric equalities for rosettes},
  author = {M. Zwierzyński},
  journal= {arXiv preprint arXiv:1605.08304},
  year   = {2020}
}

Comments

21 pages, 7 figures

R2 v1 2026-06-22T14:10:20.455Z