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. - STAMPA. - 163:(2022), pp. 549-576. [10.1016/j.matpur.2022.05.014]
Integral Symmetry Conditions
GIUSEPPE DEVILLANOVA
;SERGIO SOLIMINI
2022-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
