This article is cited in 1 paper

Mathematics

Directional derivative of the weight of a minimal filling in Riemannian manifolds

E. I. Stepanova

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: It is proved that the weight of the minimal filling, the Steiner–Gromov ratio, and the Steiner subratio regarded as functions of finite subsets of a complete connected Riemannian manifold have directional derivatives in all directions.

Key words: Riemannian manifold, minimal filling.

UDC: 514.77+519.176+515.165.7

Received: 11.02.2013

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2015, 70:1, 14–18

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