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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 5, Pages 1097–1105 (Mi izv1565)  

Minimal geodesics of a torus with a hole

H. Zieschang


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:2, 449–457

Bibliographic databases:

UDC: 512+517.53
MSC: Primary 30F99; Secondary 32G15, 57N05, 20H10
Received: 22.01.1985

Citation: H. Zieschang, “Minimal geodesics of a torus with a hole”, Izv. Akad. Nauk SSSR Ser. Mat., 50:5 (1986), 1097–1105; Math. USSR-Izv., 29:2 (1987), 449–457

Citation in format AMSBIB
\Bibitem{Zie86}
\by H.~Zieschang
\paper Minimal geodesics of a~torus with a~hole
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 5
\pages 1097--1105
\mathnet{http://mi.mathnet.ru/izv1565}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=873662}
\zmath{https://zbmath.org/?q=an:0619.30047}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 2
\pages 449--457
\crossref{https://doi.org/10.1070/IM1987v029n02ABEH000978}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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