Research On The Convergence Of Inversive Distance Circle Packing

This article studies the convergence problem related to inversive distance circle packing.It mainly focuses on(1)the Bowers-Stephenson conjecture regarding inversive distance circle packing,and proving that the discrete conformal mapping induced by the inversive distance circle packing converges to the Riemann mapping;(2)the convergence of the discrete uniformization mapping induced by the inversive distance circle packing metric on the torus to the classical uniformization mapping.