Geodesic
Canonical form of a two-dimensional Riemann manifold
Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 67-70.

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A proof of the existence on a Riemann manifold of a system of canonical cuts such that the canonical form of the manifold will be a convex region with the minimum number of sides. 
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     author = {Yu. M. Rodnyi},
     title = {Canonical form of a two-dimensional {Riemann} manifold},
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     year = {1971},
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}
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Yu. M. Rodnyi. Canonical form of a two-dimensional Riemann manifold. Matematičeskie zametki, Tome 9 (1971) no. 1, pp. 67-70. http://geodesic.mathdoc.fr/item/MZM_1971_9_1_a8/