文摘
We prove that every meromorphic function on the closure of an analytic Jordan domain that is sufficiently well-behaved on the boundary is conformally equivalent to a rational map whose degree is smallest possible. We also show that the minimality of the degree fails in general without the boundary assumptions. As an application, we generalize a theorem of Ebenfelt, Khavinson, and Shapiro by characterizing fingerprints of polynomial pseudo-lemniscates.