Geodesic
On the Saint-Venant conditions for quasiconformal deformations
Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 285-297

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Necessary and sufficient conditions are established for the existence of a quasiconformal deformation with specified characteristics. In essence these conditions are analogous to the Saint-Venant compatibility conditions. 
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     author = {V. I. Semenov},
     title = {On the {Saint-Venant} conditions for quasiconformal deformations},
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V. I. Semenov. On the Saint-Venant conditions for quasiconformal deformations. Sbornik. Mathematics, Tome 69 (1991) no. 1, pp. 285-297. http://geodesic.mathdoc.fr/item/SM_1991_69_1_a16/