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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