The Distortion in Conformal Mapping in Hyperbolic Geometry
الكلمات المفتاحية:
Distortion، Conformal maps، Unit disc، Sharp two-point، hyperbolic geometryالملخص
Nehari-type inequalities for normalized univalent functions are combined with elementary monotonicity arguments to give quick and simple proofs for numerous sharp two-point distortion theorems for conformal maps. These inequalities are used to prove two theorems of sharp two-point distortion theorems for conformal maps from the unit disk into the unit disk equipped with hyperbolic geometry.
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