Circular arcs are the only analytic Jordan curves with an exterior power point

In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary $c$ of a given convex body is a disk. In this paper, we use Riordan matrices to show that, if this curve $c$ is analytic, then one single exterior power point is sufficient.

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Bibliographic Details
Main Author Prieto-Martínez, Luis Felipe
Format Journal Article
LanguageEnglish
Published 18.01.2022
Subjects
Mathematics - Metric Geometry
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Summary:In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary $c$ of a given convex body is a disk. In this paper, we use Riordan matrices to show that, if this curve $c$ is analytic, then one single exterior power point is sufficient.
DOI:10.48550/arxiv.2201.07892