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