Abstract
For a nonconstant holomorphic map between projective Riemann surfaces with conformai 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.
Original language | English |
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Pages (from-to) | 41-57 |
Number of pages | 17 |
Journal | Tohoku Mathematical Journal |
Volume | 63 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2011 Mar |
Keywords
- Conformai metric
- Schwarzian derivative
- Univalence criterion
ASJC Scopus subject areas
- Mathematics(all)