Tohoku Mathematical Journal

The dimension of a cut locus on a smooth Riemannian manifold

Jin-ichi Itoh and Minoru Tanaka

Full-text: Open access

Article information

Tohoku Math. J. (2) Volume 50, Number 4 (1998), 571-575.

First available in Project Euclid: 3 May 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Digital Object Identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 28A78: Hausdorff and packing measures


Itoh, Jin-ichi; Tanaka, Minoru. The dimension of a cut locus on a smooth Riemannian manifold. Tohoku Mathematical Journal 50 (1998), no. 4, 571--575. doi:10.2748/tmj/1178224899.

Export citation


  • [1] J CHEEGER AND D. EBIN, Comparison theorems in Riemannian geometry, North-Holland, Amsterdam, 1975
  • [2] K J FALCONER, The geometry of fractal sets, Cambridge Univ Press, 198
  • [3] H GLUCKANDD SINGER, Scattering of geodesic fields I, Ann of Math 108 (1978), 347-37
  • [4] J HEBDA, Metric structure of cut loci in surfaces and Ambrose's problem, J Differential Geom 4 (1994), 621-642
  • [5] J. ITOH, The length of cut locus in a surface and Ambrose's problem, J Differential Geom 43 (1996), 642-651
  • [6] J ITOH, Riemannian metric with fractal cut locus, to appea
  • [7] V OZOLS, Cut locus in Riemannian manifolds, Thoku Math J. 26 (1974), 219-22
  • [8] J MILNOR, Morth theory, Ann of Math Studies No 51, Princeton Univ Press, 196
  • [9] F MORGAN, Geometric measure theory, A beginner's guide, Academic Press 198
  • [10] K SHIOHAMA AND M. TANAKA, The length function of geodesic parallel circles, in "Progress i Differential Geometry" (K Shiohama, ed) Adv Studies in Pure Math, Kinokuniya, Tokyo 22 (1993), 299-308
  • [11] F W WARNER, The conjugate locus of a Riemannian manifold, Amer J Math 87 (1965), 575-60