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.
@article{1303219935,
author = {Kim, Seong-A and Sugawa, Toshiyuki},
title = {Geometric invariants associated with projective structures and univalence criteria},
journal = {Tohoku Math. J. (2)},
volume = {63},
number = {1},
year = {2011},
pages = { 41-57},
language = {en},
url = {http://dml.mathdoc.fr/item/1303219935}
}
Kim, Seong-A; Sugawa, Toshiyuki. Geometric invariants associated with projective structures and univalence criteria. Tohoku Math. J. (2), Tome 63 (2011) no. 1, pp. 41-57. http://gdmltest.u-ga.fr/item/1303219935/