Generalized Ahlfors functions |
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| Authors: | Miran Cerne Manuel Flores |
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| Affiliation: | Department of Mathematics, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia ; Department of Mathematics, University of La Laguna, 38771 La Laguna, Tenerife, Spain |
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| Abstract: | Let  be a bordered Riemann surface with genus  and  boundary components. Let  be a smooth family of smooth Jordan curves in  which all contain the point 0 in their interior. Let  and let  be the family of all bounded holomorphic functions  on  such that  and  for almost every  . Then there exists a smooth up to the boundary holomorphic function  with at most  zeros on  so that  for every  and such that  for every  . If, in addition, all the curves  are strictly convex, then  is unique among all the functions from the family  . |
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| Keywords: | Bordered Riemann surface Ahlfors function Riemann-Hilbert problem |
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