Geodesic
Minimal geodesics of a torus with a hole
Izvestiya. Mathematics, Tome 29 (1987) no. 2, pp. 449-457 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

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