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We assign a positive number V, a new conformal invariant, to a Riemann surface R of finite genus in terms of the extremal lengths of certain weak homology classes on R, and determine the range of V. In particular we find algebraic relations among the extremal lengths of homology classes on compact Riemann surfaces.
Published Online: 2008-06-11
Published in Print: 1999-03-12
© Walter de Gruyter