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2007 Schwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map
Annalisa Calini, Joel Langer
Experiment. Math. 16(3): 321-346 (2007).

Abstract

A local normal form is obtained for geodesics in the space $\Lambda=\{\Gamma\}$ of analytic Jordan curves in the extended complex plane with symmetric space multiplication $\Gamma_1\cdot\Gamma_2$ defined by Schwarzian reflection of $\Gamma_2$ in $\Gamma_1$. Local geometric features of $(\Lambda, \cdot)$ will be seen to reflect primarily the structure of the Witt algebra, while issues of global behavior of the exponential map will be viewed in the context of conformal mapping theory.

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Annalisa Calini. Joel Langer. "Schwarz Reflection Geometry II: Local and Global Behavior of the Exponential Map." Experiment. Math. 16 (3) 321 - 346, 2007.

Information

Published: 2007
First available in Project Euclid: 7 March 2008

zbMATH: 1132.53029
MathSciNet: MR2367322

Subjects:
Primary: 30D05, 53A30, 53C35

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.16 • No. 3 • 2007
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