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Let T g be the Teichmϋller space and R g the Riemann space of compact Riemann surfaces of genus g with g = 2. The space R g can be realized as the quotient of T g by a properly discontinuous group M g , the modular group. Various metrics have been defined for T g which are compatible with the standard topology for T g and induce quotient metrics for R g . Several authors have considered the Weil-Petersson metric for T g . A length estimate derived in a previous paper is summarized; combiningdoi:10.2140/pjm.1977.70.281 fatcat:druseqm5nbcvxl5xvqe7khhbua