Comptes Rendus
no. 11
Mathematical analysis
Periods of L2-forms in an infinite-connected planar domain

Presented by: Gilles Pisier

Mikhail Dubashinskiy1
1 Chebyshev Laboratory, St. Petersburg State University, 14th Line 29b, Vasilyevsky Island, Saint Petersburg 199178, Russia
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1060-1064.

Let Ω⊂R2 be a countably-connected domain. In Ω, consider closed differential forms of degree 1 with components in L2(Ω). Further, consider sequences of periods of such forms around holes in Ω, i.e. around bounded connected components of R2∖Ω. For which domains Ω the collection of such a period sequences coincides with ℓ2? We give an answer in terms of metric properties of holes in Ω.

Soit Ω⊂R2 un domaine infiniment connexe. Considérons des formes différentielles fermées dans Ω de degré 1 et à composantes dans L2(Ω). Considérons de plus les suites de périodes de formes telles autour de trous dans le domaine Ω, c'est-à-dire autour des composantes connexes bornées de R2∖Ω. Quels sont les domaines Ω tels que l'ensemble de ces suites de periodes coïncide avec ℓ2 ? On obtient un critère en termes de propriétés métriques des trous dans Ω.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.09.007

Mikhail Dubashinskiy 1

1 Chebyshev Laboratory, St. Petersburg State University, 14th Line 29b, Vasilyevsky Island, Saint Petersburg 199178, Russia 
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Mikhail Dubashinskiy. Periods of L2-forms in an infinite-connected planar domain. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1060-1064. doi : 10.1016/j.crma.2016.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.007/

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