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

Goldman, Michael; Merlet, Benoît

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.4171/RMI/1504

Title :

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

Author(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]

Journal title :

Revista Matemática Iberoamericana

Pages :

2073-2094

Publisher :

European Mathematical Society

Publication date :

2024-10-03

ISSN :

0213-2230

HAL domain(s) :

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

English abstract : [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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

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

Collections :