On the partition of the 2-sphere by geodesic nets
HTML articles powered by AMS MathViewer
- by Aladár Heppes PDF
- Proc. Amer. Math. Soc. 127 (1999), 2163-2165 Request permission
Abstract:
The main result of the paper is that for every natural number $n$ there exists a geodesic net with vertices of degree 3 or 4 partitioning the round 2-sphere into $n$ regions.References
- Christopher B. Croke, Poincaré’s problem and the length of the shortest closed geodesic on a convex hypersurface, J. Differential Geometry 17 (1982), no. 4, 595–634 (1983). MR 683167
- Joel Hass and Frank Morgan, Geodesics and soap bubbles in surfaces, Math. Z. 223 (1996), no. 2, 185–196. MR 1417428, DOI 10.1007/PL00004560
- Joel Hass and Frank Morgan, Geodesic nets on the $2$-sphere, Proc. Amer. Math. Soc. 124 (1996), no. 12, 3843–3850. MR 1343696, DOI 10.1090/S0002-9939-96-03492-2
- A. Heppes, Isogonale sphärische Netze, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 7 (1964), 41–48 (German). MR 173193
Additional Information
- Aladár Heppes
- Affiliation: Vércse u. 24/A, H-1124 Budapest, Hungary
- Email: h9202hep@helka.iif.hu
- Received by editor(s): October 21, 1997
- Published electronically: March 17, 1999
- Additional Notes: The author was partially supported by the Hungarian National Science Foundation.
- Communicated by: Christopher Croke
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2163-2165
- MSC (1991): Primary 53C22; Secondary 53A10
- DOI: https://doi.org/10.1090/S0002-9939-99-04966-7
- MathSciNet review: 1618690