In this paper, we consider smooth, closed, strictly convex curves contained inside the unit circle T 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 (a chain of Poncelet ellipses). We apply these results to operators that are compressions of the shift operator on model spaces and describe necessary and sufficient conditions for the numerical range to contain 0. (C) 2021 Elsevier Inc. All rights reserved.
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