Let Ω ⊂ ℝ2 be a countably connected domain. With any closed differential form of degree 1 in Ω with components in L2(Ω) one associates the sequence of its periods around the holes in Ω that is around the bounded connected components of ℝ2 \ Ω. For which Ω the collection of such period sequences coincides with ℓ2 We give an answer in terms of metric properties of holes in Ω.
Scopus subject areas
- Geometry and Topology