Algebraic Relations among Extremal Lengths of Homology Classes on Compact Riemann Surfaces
Makoto Masumoto · Mathematische Nachrichten · 2002
We show that the extremal lengths of singular homology classes on a compact Riemann surface satisfy algebraic equations depending only on the genus of the surface. We apply these algebraic relations to prove a theorem on the distribution of diagonal entries of normalized period matrices of a compact Riemann surface of genus two, which shows a new symmetry of such surfaces.