Geometric invariants associated with projective structures and univalence criteria

Details Geometric invariants associated with projective structures and univalence criteria Geometric invariants associated with projective structures and univalence criteria

2009-12-02

arxiv.org/abs/0912.0344v1

Mathematics

Complex Variables

16 pages

Scientific paper

For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are related by the "Schwarzian derivative" of the metrics of the surfaces (at least for the case of virtual orders 2 and 3). As an application, we give univalence criteria for a meromorphic function on the unit disk in terms of the projective Schwarzian derivative of virtual order 3.

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