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Comptes Rendus Mathématique
Volume 354, n° 11
pages 1060-1064 (novembre 2016)
Doi : 10.1016/j.crma.2016.09.007
Received : 29 January 2016 ;  accepted : 14 September 2016
Periods of L 2-forms in an infinite-connected planar domain
Périodes de formes L 2 dans un domaine plan infiniment connexe

Mikhail Dubashinskiy 1, 2
 Chebyshev Laboratory, St. Petersburg State University, 14th Line 29b, Vasilyevsky Island, Saint Petersburg 199178, Russia 


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

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Soit   un domaine infiniment connexe. Considérons des formes différentielles fermées dans Ω de degré 1 et à composantes dans  . 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  . Quels sont les domaines Ω tels que l'ensemble de ces suites de periodes coïncide avec   ? On obtient un critère en termes de propriétés métriques des trous dans Ω.

The full text of this article is available in PDF format.
1  Fax: +7 (812) 363 68 71.
2  The work is supported by the Russian Science Foundation grant 14-21-00035.

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