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.
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The authors thank the anonymous referees for helpful suggestions.
Malik Younsi supported by NSERC.
Communicated by Edward B. Saff.
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Richards, T., Younsi, M. Conformal Models and Fingerprints of Pseudo-lemniscates. Constr Approx 45, 129–141 (2017). https://doi.org/10.1007/s00365-016-9348-0
- Meromorphic functions
- Conformal welding
- Conformal models
Mathematics Subject Classification
- Primary 30C35
- Secondary 37E10