English

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

Metric Geometry 2022-07-05 v2

Abstract

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

Keywords

Cite

@article{arxiv.2201.07892,
  title  = {Circular arcs are the only analytic Jordan curves with an exterior power point},
  author = {Luis Felipe Prieto-Martínez},
  journal= {arXiv preprint arXiv:2201.07892},
  year   = {2022}
}

Comments

There is a mistake in the proof of the main theorem that spoils the strategy for showing uniqueness. At this moment I am not able to ensure the vality of the main theorem