Geodesic
Univalent Meromorphic Differentials on Riemann Surfaces of Types $(g,n)$
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 1, pp. 73-84

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In this article given construction all types univalent meromorphic differentials on Riemann surfaces with finite numbers of punctures. Proven, that non exists gaps by Weierstrass and by Noether. Dimensions factor space of meromorphic differentials third kind with finite numbers poles first order by subspace exact holomorphic differentials are given. In particular, dimension first holomorphic de Rham cohomology group of differentials are given. Two examples non constant holomorphic functions without zeros on such surfaces are constructed. For special class of functions proved Abel's theorem. 
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     author = {A. N. Chichkakova and V. V. Chueshev},
     title = {Univalent {Meromorphic} {Differentials} on {Riemann} {Surfaces} of {Types} $(g,n)$},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
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A. N. Chichkakova; V. V. Chueshev. Univalent Meromorphic Differentials on Riemann Surfaces of Types $(g,n)$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 1, pp. 73-84. http://geodesic.mathdoc.fr/item/VNGU_2009_9_1_a7/