In this paper we extend to the case of a generic dimension N>= 2 some notions introduced in a previous article to establish some new variational methods. Such notions relay on the concept of higher order barycenters of a positive measure and allow to give some symmetry conditions which in two dimension lead to the conclusions that the measures which satisfy them in a suitable optimal way are uniformly concentrated on the vertices of a regular polygon. Here, investigating the extension of such properties to the case of a general dimension, we mainly focus on the geometrical and algebraic aspects, including some connections with Platonic Solids regardless any further application to variational methods.

Integral Symmetry Conditions / Devillanova, Giuseppe; Solimini, Sergio Fausto Libero. - STAMPA. - (2020).

Integral Symmetry Conditions

GIUSEPPE DEVILLANOVA
;
SERGIO SOLIMINI
2020-01-01

Abstract

In this paper we extend to the case of a generic dimension N>= 2 some notions introduced in a previous article to establish some new variational methods. Such notions relay on the concept of higher order barycenters of a positive measure and allow to give some symmetry conditions which in two dimension lead to the conclusions that the measures which satisfy them in a suitable optimal way are uniformly concentrated on the vertices of a regular polygon. Here, investigating the extension of such properties to the case of a general dimension, we mainly focus on the geometrical and algebraic aspects, including some connections with Platonic Solids regardless any further application to variational methods.
2020
Integral Symmetry Conditions / Devillanova, Giuseppe; Solimini, Sergio Fausto Libero. - STAMPA. - (2020).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/209291
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