  The question of convergence of iterated integrals on Riemann surfaces goes
back to Bloch, Levin, and Zagier, who have proved this fact for various
iterated integrals in the context of elliptic curves. In this work, I prove the
convergence of the iterated integral defining Bloch-Wigner function on higher
genus curves, utilizing some novel results of Hou in the theory of Schottky
uniformization of Riemann surfaces, as well as some classical results of Bers
and more recent results of Nayatani on Poincare metrics on domains of
discontinuity of Kleinian groups.
