Horocycles on Riemann surfaces
HTML articles powered by AMS MathViewer
- by Mika Seppälä and Tuomas Sorvali PDF
- Proc. Amer. Math. Soc. 118 (1993), 109-111 Request permission
Abstract:
By the Collar Theorem, every puncture on a hyperbolic Riemann surface with punctures has a horocyclic neighborhood of area $2$. Furthermore two such neighborhoods associated to different punctures are disjoint. This result can be improved if we omit the condition that horocyclic neighborhoods of different punctures must be disjoint. Using arguments of the second author we show, in this paper, that each puncture of a hyperbolic Riemann surface has a horocyclic neighborhood of area $4$.References
- Peter Buser, Geometry and spectra of compact Riemann surfaces, Progress in Mathematics, vol. 106, Birkhäuser Boston, Inc., Boston, MA, 1992. MR 1183224 Noami Halpern, Some contributions to the theory of Riemann surfaces, Thesis, Columbia University, 1978.
- Linda Keen, Collars on Riemann surfaces, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973) Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974, pp. 263–268. MR 0379833
- Irwin Kra, Horocyclic coordinates for Riemann surfaces and moduli spaces. I. Teichmüller and Riemann spaces of Kleinian groups, J. Amer. Math. Soc. 3 (1990), no. 3, 499–578. MR 1049503, DOI 10.1090/S0894-0347-1990-1049503-1
- Tuomas Sorvali, Quasiconformally equivalent polygons, Joensuun Korkeakoulun Julkaisuja, Sarja B, No. 5. [Publications of the University of Joensuu, Series B, No. 5], University of Joensuu, Joensuu, 1973. MR 0447566
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 109-111
- MSC: Primary 30F45; Secondary 51M10, 53A35
- DOI: https://doi.org/10.1090/S0002-9939-1993-1128730-3
- MathSciNet review: 1128730