Ahlfors extremals realizing the gonality
Ahlfors extremals realizing the gonality
Let a compact bordered Riemann surface have gonality equal to the least degree of a conformal map to the disc, and let denote an Ahlfors extremal function associated with two marked points, with the limiting one-point extremal. Ahlfors gonality conjecture. Any conformal mapping realizing the gonality arises as an Ahlfors extremal function , perhaps after coalescing two points to obtain an Ahlfors map maximizing the modulus of the derivative at . The source records the question as unsettled; it is proved there only in the hyperelliptic case.
Sources & referencesView supporting material
Primary source
Alexandre Gabard, “Notes on Hilbert's 16th: experiencing Viro's theory”, arXiv:1310.1865 (2013).
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