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Mobius parametrizations of curves in R-n
(BIRKHAUSER VERLAG AG, 2009)
We use Ahlfors' definition of Schwarzian derivative for curves in euclidean spaces to present new results about Mobius or projective parametrizations. The class of such parametrizations is invariant under compositions with ...
General criteria for curves to be simple
(2018)
We extend previous results for parametrized curves in euclidean space to be simple. The new condition depends as before on Ahlfors' Schwarzian and considers a conformal metric on a given interval and the new diameter. We ...
Finding complete conformal metrics to extend conformal mappings
(INDIANA UNIV MATH JOURNAL, 1998)
This paper shows how new differential geometric approaches to univalence criteria involving the Schwarzian derivative can be applied to a classical, but very general, criterion of Nehari. We show how positive solutions to ...