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.
Scopus subject areas
- Geometry and Topology