# Ahlfors circle maps and total reality: from Riemann to Rohlin

@article{Gabard2012AhlforsCM, title={Ahlfors circle maps and total reality: from Riemann to Rohlin}, author={A. Gabard}, journal={arXiv: History and Overview}, year={2012} }

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known intersection with real algebraic geometry, especially Klein's ortho-symmetric curves via the paradigm of {\it total reality}. This leads to a gallery of pictures quite pleasant… Expand

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