Sur la forme de la boule unité de la norme stable unidimensionnelle

Details Sur la forme de la boule unité de la norme stable unidimensionnelle Sur la forme de la boule unité de la norme stable unidimensionnelle

2005-02-22

arxiv.org/abs/math/0502454v1

Manuscripta Mathematica 119 (2006) 347-358

Mathematics

Differential Geometry

13 pages, in French

Scientific paper

10.1007/s00229-005-0622-x

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are completely described by combinatorial properties of the graph. We study then the realizable forms as stable ball of Riemannan manifolds of dimension larger than three. For a Riemannian manifold $(M, g)$ fixed, we show that a broad class of polytopes can appear as stable ball of metrics in the conformal class of $g$. We use for that a polyhedral technique.

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