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

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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. 
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     author = {G. V. Kuz'mina},
     title = {On existence of quadratic differentials with poles of high orders},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {129--138},
     publisher = {mathdoc},
     volume = {212},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_212_a8/}
}
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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/