Old and New on the Schwarzian Derivative

Brad Osgood
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Brad Osgood: Stanford University, Department of Mathematics

A chapter in Quasiconformal Mappings and Analysis, 1998, pp 275-308 from Springer

Abstract: Abstract Let f be an analytic function. We define its Schwarzian derivative to be 1.1 $$Sf = {{\left( {\frac{{f''}}{{f'}}} \right)}^{{\prime \prime }}} - \frac{1}{2}{{\left( {\frac{{f''}}{{f'}}} \right)}^{2}} = \frac{{f'''}}{{f'}} - \frac{3}{2}{{\left( {\frac{{f''}}{{f'}}} \right)}^{2}}. $$ The classical notation is {f, z}, or{w, z}if we write w= f(z), and is due to Cayley in an 1880 paper [19]. Cayley was also the one to honor Schwarz with the appellation.

Keywords: Connected Domain; Quasiconformal Mapping; Bergman Kernel; Monodromy Group; Schwarzian Derivative (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-0605-7_16

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