Optimal arrangement of finite point sets in Riemannian 2-manifolds (Q2736072)

The author announces two theorems without proof and describes three applications. The first theorem extends L. Fejes Tóth's theorem on sums of moments to Riemannian 2-manifolds, as an asymptotic relation, and it provides an inverse in the form of a stability result, leading to almost regular hexagonal patterns. The second theorem states that certain special point sequences give good arrangements in the sense of the first theorem, and that most sequences (in the Baire category sense) give rather good arrangements.NEWLINENEWLINENEWLINEAn extended version of Theorem 1 with detailed proofs and generalized versions of the applications the author has published in Geom. Dedicata 84, No.~1-3, 271-320 (2001; Zbl 0982.52020).NEWLINENEWLINEFor the entire collection see [Zbl 0967.00102].