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Genus 3 normal coverings of the Riemann sphere branched over 4 points.

Yolanda Fuertes, Manfred Streit (2006)

Revista Matemática Iberoamericana

In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.

Geometric characterization for affine mappings and Teichmüller mappings

Zhiguo Chen (2003)

Studia Mathematica

We characterize affine mappings on the unit disk and on rectangles by module conditions. The main result generalizes the classic Schwarz lemma. As an application, we give a sufficient condition for a K-quasiconformal mapping on a Riemann surface to be a Teichmüller mapping.

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