Geometry & Topology Volume 11, issue 2 (2007)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Procedure

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Other MSP Journals

Shapes of geodesic nets

Alexander Nabutovsky and Regina Rotman

Geometry & Topology 11 (2007) 1225–1254

DOI: 10.2140/gt.2007.11.1225

Bibliography

1	V Bangert, On the existence of closed geodesics on two-spheres, Internat. J. Math. 4 (1993) 1 MR1209957
2	C B Croke, Area and the length of the shortest closed geodesic, J. Differential Geom. 27 (1988) 1 MR918453
3	J Franks, Geodesics on $S^2$ and periodic points of annulus homeomorphisms, Invent. Math. 108 (1992) 403 MR1161099
4	D Gromoll, W Meyer, On differentiable functions with isolated critical points, Topology 8 (1969) 361 MR0246329
5	M Gromov, Filling Riemannian manifolds, J. Differential Geom. 18 (1983) 1 MR697984
6	J Hass, F Morgan, Geodesic nets on the $2$-sphere, Proc. Amer. Math. Soc. 124 (1996) 3843 MR1343696
7	N Hingston, On the growth of the number of closed geodesics on the two-sphere, Internat. Math. Res. Notices (1993) 253 MR1240637
8	A B Katok, Ergodic perturbations of degenerate integrable Hamiltonian systems, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 539 MR0331425
9	A Nabutovsky, R Rotman, Volume, diameter and the minimal mass of a stationary 1-cycle, Geom. Funct. Anal. 14 (2004) 748 MR2084979
10	A Nabutovsky, R Rotman, The minimal length of a closed geodesic net on a Riemannian manifold with a nontrivial second homology group, Geom. Dedicata 113 (2005) 243 MR2171308
11	H B Rademacher, On the average indices of closed geodesics, J. Differential Geom. 29 (1989) 65 MR978076
12	R Rotman, The length of a shortest geodesic net on a closed Riemannian manifold, Topology 46 (2007) 343
13	R Rotman, Flowers on Riemannian manifolds
14	M Vigué-Poirrier, D Sullivan, The homology theory of the closed geodesic problem, J. Differential Geometry 11 (1976) 633 MR0455028
15	W Ziller, Geometry of the Katok examples, Ergodic Theory Dynam. Systems 3 (1983) 135 MR743032