Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus

  • A. P. Pal-Val

Анотація

2-dimensional compact oriented Riemannian manifolds $M_\varepsilon$ consisting of one or several copies of some base surface $\Gamma$ with a large number of thin tubes, endowed with a metric depending on a small parameter $\varepsilon$ are considered. The asymptotic behaviour of harmonic 1-forms on $M_\varepsilon$ is studied when the number of tubes increases and their thickness vanishes, as $\varepsilon\to 0$. We obtain the homogenized equations on the base surface $\Gamma$ describing the leading term of the asymptotics.

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(1)
A. P. Pal-Val, Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus, Мат. физ. анал. геом. 6 (1999), 323-352.

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