Rocky Mountain Journal of Mathematics

On Riemannian surfaces with conical singularities

Charalampos Charitos, Ioannis Papadoperakis, and Georgios Tsapogas

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Abstract

The geometry of closed surfaces of genus $g\geq 2$ equipped with a Riemannian metric of variable bounded curvature with finitely many conical points is studied. The main result is that the set of closed geodesics is dense in the space of geodesics.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 5 (2018), 1455-1474.

Dates
First available in Project Euclid: 19 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1539936031

Digital Object Identifier
doi:10.1216/RMJ-2018-48-5-1455

Mathematical Reviews number (MathSciNet)
MR3866554

Zentralblatt MATH identifier
06958787

Subjects
Primary: 53C22: Geodesics [See also 58E10] 57M50: Geometric structures on low-dimensional manifolds

Keywords
Riemannian surfaces conical singularities Gromov hyperbolicity non-unique geodesics

Citation

Charitos, Charalampos; Papadoperakis, Ioannis; Tsapogas, Georgios. On Riemannian surfaces with conical singularities. Rocky Mountain J. Math. 48 (2018), no. 5, 1455--1474. doi:10.1216/RMJ-2018-48-5-1455. https://projecteuclid.org/euclid.rmjm/1539936031


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References

  • W. Ballmann, Lectures on spaces of non positive curvature, Birkhäuser, Berlin, 1995.
  • M. Bridson and A. Haefliger, Metric spaces of non-positive curvature, Grundl. Math. Wissen. 319 (1999).
  • M. Coornaert, Sur les gropes proprement discontinus d'isometries des espaces hyperboliques au sens de Gromov, M.S. thesis, Univ. Louis-Pasteur, Strasbourg, France, 1990.
  • M. Coornaert, T. Delzant and A. Papadopoulos, Géometrie et théorie des groupes, Lect. Notes Math. 1441 (1980).
  • M. Gromov, Hyperbolic groups, in Essays in group theory, MSRI 8 (1987), 75–263.
  • M. Gromov, J. Lafontaine and P. Pansu, Structures metriques pour les variétés Riemanniennes, Fernand Nathan, Paris, 1981.
  • F. Paulin, Constructions of hyperbolic groups via hyperbolization of polyhedra, in Group theory from a geometrical viewpoint, E. Ghys and A. Haefliger, eds., World Scientific, Singapore, 1991.
  • M. Troyanov, Les surfaces euclidiennes a singularites coniques, Enseign. Math. 32 (1986), 79–94.
  • ––––, Prescribing curvature on compact surfaces with conical singularities, Trans. Amer. Math. Soc. 324, 793–821.
  • A. Zorich, Flat surfaces, in Frontiers in number theory, physics, and geometry, P. Cartier, et al., eds., Springer-Verlag, Berlin, 2006.