Kreispackungen und Triangulierungen. (Circle packings and triangulations) (Q1803621)

This paper gives an alternative proof for the following results by E. M. Andreev, generalized by W. Thurston: Any given triangulation of the 2- sphere can be realized as the nerve of a circle packing, and this circle packing is unique up to Möbius transformations. The solution is presented by the maximum of a concave functional \(L\) on \([0,\pi]^ S\) where \(S\) is the set of sectors of the triangles and where \(L\) can be expressed in terms of the Lobatchevsky function.