Geodesic
On existence of quadratic differentials with poles of high orders
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 12, Tome 212 (1994), pp. 129-138 
G. V. Kuz'mina. On existence of quadratic differentials with poles of high orders. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 12, Tome 212 (1994), pp. 129-138. http://geodesic.mathdoc.fr/item/ZNSL_1994_212_a8/
@article{ZNSL_1994_212_a8,
     author = {G. V. Kuz'mina},
     title = {On existence of quadratic differentials with poles of high orders},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--138},
     year = {1994},
     volume = {212},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_212_a8/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Conditions of existence of a quadratic differential which has poles of high orders at the points $c_k$, $k=1,\dots,p$, and is the limit of a sequence of quadratic differentials of a special type are established. The quadratic differential mentioned has no poles of order greater than 2 and has poles of order 2 at the points situated in a suitable uniform way on the circles $|z-c_k|=\varepsilon_k$, $\varepsilon_k\to0$, $k=1,\dots,p$. Bibliography: 9 titles.