Geodesic
Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 3, pp. 323-352 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

$2$-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_3_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},
     year = {1999},
     volume = {6},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a9/}
}
TY  - JOUR
AU  - A. P. Pal-Val
TI  - Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 1999
SP  - 323
EP  - 352
VL  - 6
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a9/
LA  - en
ID  - JMAG_1999_6_3_a9
ER  - 
%0 Journal Article
%A A. P. Pal-Val
%T Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 1999
%P 323-352
%V 6
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a9/
%G en
%F JMAG_1999_6_3_a9
A. P. Pal-Val. Asymptotic behaviour of harmonic 1-forms on Riemannian surfaces of increasing genus. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (1999) no. 3, pp. 323-352. http://geodesic.mathdoc.fr/item/JMAG_1999_6_3_a9/