On potential theoretic skeletons of polyhedra (Q1302139)

The authors prove the existence of the potential theoretic skeleton called mother body for any polyhedron in two dimensions. The term mother body was used by \textit{D. Zidarov} [see for example, Inverse gravimetric problem in geoprospecting and geodesy, Elsevier, Amsterdam (1990; Zbl 0718.31001)] and more precisely by \textit{B. Gustafsson} [SIAM J. Math. Anal. 29, 1106-1117 (1998; Zbl 0913.31002)]. For polyhedra in arbitrary dimension the authors prove that the mother bodies are in one to one correspondence with certain type of decompositions of the polyhedron into convex subpolyhedra. The question of existence of a mother body for arbitrary polyhedra in higher dimensions is still open.