Bergman coordinates on finite Riemann surfaces
Abstract
Bergman coordinates on finite Riemann surfaces are defined. It is proved that they extend meromorphically to the double of the surface. A proof of an analogue of Bell’s Density Lemma for finite Riemann surfaces is given. Embeddability of a finite Riemann surface in [special characters omitted]3 (or [special characters omitted]2) by means of Bergman coordinate functions is studied. Finally, a proof of existence of a primitive pair for the double of a finite Riemann surface consisting of Ahlfors maps is given.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Mathematics
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