A general conformal geometric reflection principle

Roth, Oliver

doi:10.1090/S0002-9947-07-03942-6

A general conformal geometric reflection principle
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Trans. Amer. Math. Soc. 359 (2007), 2501-2529 Request permission

Abstract:

We prove a generalization of the Schwarz–Carathéodory reflec- tion principle for analytic maps $f$ from the unit disk into arbitrary Riemann surfaces equipped with a complete real analytic conformal Riemannian metric $\lambda (w) |dw|$. This yields a necessary and sufficient condition for $f$ to have an analytic continuation in terms of the pullback of the metric $\lambda (w) |dw|$ under the map $f$.

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