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http://dx.doi.org/10.4134/CKMS.2008.23.4.577

A NOTE ON THE VOLUME COMPARISON OF TUBES AROUND GEODESICS  

Yun, Jong-Gug (DEPARTMENT OF MATHEMATICS EDUCATION KOREA NATIONAL UNIVERSITY OF EDUCATION)
Publication Information
Communications of the Korean Mathematical Society / v.23, no.4, 2008 , pp. 577-585 More about this Journal
Abstract
In this paper, we shall calculate the volume of normal tubes around geodesics under a curvature perturbation to establish a theorem of volume comparison type.
Keywords
mean curvature; sectional curvature;
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  • Reference
1 S. Gallot, Isoperimetric inequalities based on integral norms of Ricci curvature, Asterisque 18 (1983), 191-216
2 S. Gallot, D. Hullin, and J. Lafontain, Riemannian Geometry, Springer-Verlag
3 A. Gray, Tubes, Birkhauser Verlag, 2004
4 R. Bishop, A relation between volume, mean curvature and diameter, Notices Amer. Math. Soc. 10 (1963), 364
5 I. Chavel, Eigen Values in Riemannian Geometry, Academic press, 1984
6 J.-G. Yun, Mean curvature comparison with $L^{1}$-norms of Ricci curvature, Canad. Math. Bull. 49 (2006), no. 1, 152-160   DOI
7 D. Yang, Convergence of Riemannain manifolds with Integral bounds on curvature I, Ann. Sci. Ecol. Norm. Sup. 25 (1992), 77-105   DOI
8 P. Petersen, S. Shteingold, and G. Wei, Comparison geometry with integral curvature bounds, Geom. Funct. Anal. 7 (1997), 1011-1030   DOI
9 E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. Ecol. Norm. Sup. 11 (1978), 451-470   DOI
10 S.-H. Paeng, A sphere theorem under a curvature perturbation II, Kyushu J. Math. 52 (1998), 439-454   DOI   ScienceOn