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

Abstract

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.

arXiv commentThere 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