Geometric invariants associated with projective structures and univalence criteria

Seong A. Kim, Toshiyuki Sugawa

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)41-57
Number of pages17
JournalTohoku Mathematical Journal
Issue number1
Publication statusPublished - 2011 Mar


  • Conformai metric
  • Schwarzian derivative
  • Univalence criterion

ASJC Scopus subject areas

  • Mathematics(all)


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