APOLLONIAN CIRCLE PACKINGS AND CLOSED HOROSPHERES ON HYPERBOLIC 3-MANIFOLDS

摘要

A set of four mutually tangent circles in the plane with distinct points of tangency is called a Descartes configuration. Given a Descartes configuration, one can construct four new circles, each of which is tangent to three of the given ones. Continuing to repeatedly fill the interstices between mutually tangent circles with further tangent circles, we arrive at an infinite circle packing. It is called an Apollonian circle packing, after the great geometer Apollonius of Perga (262-190 BC).