The aim of this note is to relate the classical Schwarzian derivative and the geometry of Lorentz surfaces of constant curvature. 1. The starting point of our investigations lies in the following remark (joint work with L. Guieu). Consider a curve y = f(x) in the Lorentz plane with metric g = dxdy. If f (x) > 0, then its Lorentz curvature can be computed : ̺(x) = f (x) (f (x)) and enjoys the qui...

By considering integral bounds on the Schwarzian derivative we extend previous results on sufficient conditions for curves in euclidean spaces to be simple or unknotted. The conditions are optimal.

Let S H f be the Schwarzian derivative of a univalent harmonic function id="M2"> in unit disk id="M3"> D , compatible with finitely generated Fuchsian group id="M4"> G second kind. W...