Geodesic
Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 323-352.

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$2$-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. 
@article{JMAG_1999_6_a9,
     author = {A. P. Pal-Val},
     title = {Asymptotic behaviour of harmonic 1-forms on {Riemannian} surfaces of increasing genus},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {323--352},
     publisher = {mathdoc},
     volume = {6},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_a9/}
}
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A. P. Pal-Val. Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999), pp. 323-352. http://geodesic.mathdoc.fr/item/JMAG_1999_6_a9/