منابع مشابه
Sharp Distortion Theorems Associated with the Schwarzian Derivative
These are well known and important theorems of Nehari, Ahlfors and Weill, and Krauss. We refer to Lehto's book [8] for a discussion of these results and for the properties of the Schwarzian that we shall need. The constants 2 in (1.1) and 6 in (1.3) are sharp. An example for the latter is the Koebe function k(z) = z(l — z)~ which has Schwarzian Sk(z) = — 6/(1 —z). We also remark that the class ...
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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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2011
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2011.254.101