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The geometry of Euclidean surfaces with conical singularities

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Abstract

The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points. Dynamical properties for the space of geodesics are also proved.

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Authors and Affiliations

  1. Agricultural University of Athens, Athens, Greece

    Charalampos Charitos & Ioannis Papadoperakis

  2. University of the Aegean, Samos, Greece

    Georgios Tsapogas

Authors
  1. Charalampos Charitos
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  2. Ioannis Papadoperakis
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  3. Georgios Tsapogas
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Correspondence to Georgios Tsapogas.

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Charitos, C., Papadoperakis, I. & Tsapogas, G. The geometry of Euclidean surfaces with conical singularities. Math. Z. 284, 1073–1087 (2016). https://doi.org/10.1007/s00209-016-1688-8

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  • DOI: https://doi.org/10.1007/s00209-016-1688-8

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