Curves of Geodesic Centers and Poncelet Ellipses
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 of Functional Analysis
Gorkin, Pamela and Adams, Gregory. "Curves of Geodesic Centers and Poncelet Ellipses." (2021) .