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- W585607263 abstract "A theory of Schwarzian is developed based on a curve-theoretic quantity called the Schwarzian derivative of curves. The relationship between the Schwarzian and Mobius transformations is made clear. As application of the theory various injectivity theorems are obtained. 0. Introduction The Schwarzian derivative of holomorphic functions, S z = f'~) _'i(f(z))2 r< ) f'(z) 2 f'(z) ' has been generalized by several authors from various viewpoints ([1], [3], [7], [8], [10], [12], [13]). In this paper, we give a framework which unifies these generalizations. The theory is based on a curve-theoretic differential operator called the Schwarzian derivative of curves whose properties are investigated in Section 1. The Schwarzian derivative of a curve decomposes into two components. Roughly speaking, the 0-part of the Schwarzian derivative controls the parametrization of the curve while the 2-part controls itsshape. A curve with vanishing Schwarzian, which 2000 Mathematics Subject Classification: Primary 53A30; Secondary 30C55, 53A55, 53C20." @default.
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- W585607263 date "2000-01-01" @default.
- W585607263 modified "2023-09-24" @default.
- W585607263 title "CIRCULAR GEOMETRY AND THE SCHWARZIAN" @default.
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