Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle

Goldman, Michael; Merlet, Benoît

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4171/RMI/1504

Titre :

Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle

Auteur(s) :

Goldman, Michael [Auteur]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]
Merlet, Benoît [Auteur]

Reliable numerical approximations of dissipative systems [RAPSODI]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Revista Matemática Iberoamericana

Pagination :

2073-2094

Éditeur :

European Mathematical Society

Date de publication :

2024-10-03

ISSN :

0213-2230

Discipline(s) HAL :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]

Résumé en anglais : [en]

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets ...
Lire la suite >We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite perimeter in their ``measure theoretic" connected components due to Ambrosio, Caselles, Masnou and Morel. It can also be seen as a variant of the decomposition of integral currents in indecomposable components by Federer.As opposed to previous results, we do not assume that G is boundedly compact. Therefore we cannot rely on the compactness of sequences of chains with uniformly bounded N-norms. We deduce instead the result from a new abstract decomposition principle. As in earlier proofs a central ingredient is the validity of an isoperimetric inequality. We obtain it here using the finiteness of some h-mass to replace integrality.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Projet ANR :

Optimisation de forme
Centre Européen pour les Mathématiques, la Physique et leurs Interactions

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