Curves of Geodesic Centers and Poncelet Ellipses

Publication Date

Fall 10-15-2021

Description

In this paper, we consider smooth, closed, strictly convex curves contained inside the unit circle and their associated curves of geodesic centers (or dual curves). We obtain a formula for the boundary and envelope of the union of the region bounded by the geodesic circles associated with our curves. This description includes a formula for the boundary of the hyperbolic convex hull of points identified by finite Blaschke products. We describe a setting and conditions under which one can produce an infinite chain of ellipses such that each ellipse is inscribed in a convex polygon that is itself inscribed in another polygon. We apply these results to the numerical range of certain matrices.

Journal

Journal of Functional Analysis

Volume

281

Issue

8

Department

Mathematics

Second Department

Mathematics

DOI

https://doi.org/10.1016/j.jfa.2021.109110

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