arXiv subjects
Publications and source records attributed to Ilyas Bayramov.
In this note, I would like to discuss an approach to the construction of Green's function on algebraic surfaces, indicated by Manin, towards the computation of the Green's function on surfaces using Schottky uniformization. We shall see that the exact geometric interpretation of the formula mentioned there is obscure, and try to remedy the situation by investigating convergence of deformations of that formula.
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.