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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 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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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