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Differential operators associated with holomorphic mappings

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Abstract

Two differential operators which act on holomorphic mappings to complex projective space are studied. One operator is of second order and characterizes projective linear mappings. The other operator is of third order and may be viewed as a curvature. The two operators together play a role analogous to the Schwarzian derivative.

A canonical approximation to a holomorphic mapping is defined, and a relationship between the approximation and the operators is derived. In the one variable case, this reduces to a classical result relating the Schwarzian derivative and the best Möbius approximation to a holomorphic function.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada, 89154, Las Vegas, Nevada, USA

    Robert Molzon

  2. Department of Mathematics, University of Kentucky, 40506, Lexington, Kentucky, USA

    Karen Pinney Mortensen

Authors
  1. Robert Molzon
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  2. Karen Pinney Mortensen
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Communicated by E. Ruh

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Molzon, R., Mortensen, K.P. Differential operators associated with holomorphic mappings. Ann Glob Anal Geom 12, 291–304 (1994). https://doi.org/10.1007/BF02108302

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  • DOI: https://doi.org/10.1007/BF02108302

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