Geometric invariants associated with projective structures and univalence criteria

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概要

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• 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.

著者

• Sugawa Toshiyuki

  Graduate School Of Information Sciences Tohoku University

• Kim Seong-A

  Department of Mathematics Education, Dongguk University

• Kim Seong-a

  Department Of Mathematics Education Dongguk University

関連論文

• Geometric invariants associated with projective structures and univalence criteria
• On convex hyperbolic regions
• A Remark on Lowner's Theorem

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