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arXiv · 1511.07015

Interpolation by periods in planar domain

Mikhail Dubashinskiy
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Abstract

Let $Ω\subset\mathbb R^2$ be a countably connected domain. To any closed differential form of degree $1$ in $Ω$ with components in $L^2(Ω)$ one associates the sequence of its periods around holes in $Ω$, that is around bounded connected components of $\mathbb R^2\setminus Ω$. For which $Ω$ the collection of such period sequences coincides with $\ell^2$? We give the answer in terms of metric properties of holes in $Ω$.

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Mikhail Dubashinskiy. 2015-11-22. Interpolation by periods in planar domain. https://arxiv.org/abs/1511.07015

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