SUGAWA, Toshiyuki

A conformally invariant metric on Riemann surfaces associated with integrable holomorphic quadratic differentials


In this paper, we define a conformally invariant (pseudo-)metric on all Riemann surfaces in terms of integrable holomorphic quadratic differentials and analyze it. This metric is closely related to an extremal problem on the surface. As a result, we have a kind of reproducing formula for integrable quadratic differentials. Furthermore, we establish a new characterization of boundedness of geometry of hyperbolic Riemann surfaces in terms of invariant metrics.

submission: January 21, 2000

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