Seminar: Oliver Roth (G.15.25)
By a classical result of Jorgensen every geodesic in a simply connected hyperbolic domain $G$ which touches an Euclidean disk in $G$ does not intersect the interior of that disk. We give a refinement of this result that takes into account point singularities of the underlying geometric structure. As an application we extend the Gauss-Lucas-Thurston Theorem from Euclidean to hyperbolic geometry viz. from polynomials to Blaschke products.
This is joint work with Daniela Kraus, Javad Mashreghi and Annika Moucha.
