The Schwarzian derivative is a concept from complex analysis and differential geometry that arises in the study of conformal mappings and holds significant importance in the theory of univalent (or schlicht) functions.
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For a thrice differentiable function with , the Schwarzian derivative isIt vanishes exactly for fractional linear functions on intervals where the denominator does not vanish. In a two-dimensional conformal field theory, it is the inhomogeneous term in the finite conformal transformation of a stress-energy tensor with nonzero central charge.