Geodesic
Minimal geodesics of a~torus with a~hole
Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 449-457

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Let $R$ be a Riemann surface of genus $1$ with one hole. For a given homology class $\alpha\in H_1(R)$, the author determines that homotopy class within $\alpha$ which contains the shortest curve in $\alpha$. It turns out that this homotopy class is uniquely determined independently of the Riemannian metric. A conjecture of H. Cohn is thereby confirmed. Bibliography: 7 titles. 
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     author = {H. Zieschang},
     title = {Minimal geodesics of a~torus with a~hole},
     journal = {Izvestiya. Mathematics },
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H. Zieschang. Minimal geodesics of a~torus with a~hole. Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 449-457. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a8/