Infinite rigidity of inversive distance circle packings in the Poincaré disk

The maximum principle for hyperbolic inversive distance circle packings on polyhedral surfaces is established,which unifies and generalizes existing maximum principles for various types of circle packings in the literature.As an application of this principle, a discrete Schwarz-Ahlfors lemma is established.Furthermore, an infinite rigidity theorem for weighted Delaunay triangulations of the Poincaré disk is proved,which generalizes He’s hyperbolic rigidity result \cite{He2}.