Richard Rochberg
Abstract
It is known that a nonplanar Riemann surface cannot be continued into all compact Riemann surfaces of a fixed positive genus. The Poincaré metric is used to construct a conformal invariant which is used to give an essentially geometric proof of this result.
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It is known that a nonplanar Riemann surface cannot be continued into all compact Riemann surfaces of a fixed positive genus. The Poincaré metric is used to construct a conformal invariant which is used to give an essentially geometric proof of this result.
Key concepts: Riemann surface, Geometric function theory, Uniformization theorem, Conformal map, Mathematics, Continuation, Compact Riemann surface, Riemann–Hurwitz formula