논문KCI 등재
A note on the volume comparison of tubes around geodesics
대한수학회 (The Korean Mathematical Society)|2008.10|대한수학회논문집 (Communications of the KMS)|제23권 제4호|pp. 577-585
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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.
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.
참고문헌 (10)
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- S. Gallot, "Riemannian Geometry" (1980), Springer-Verlag
- A. Gray, "Tubes" (2004), Birkhauser Verlag
- E. Heintze, "A general comparison theorem with applications to volume estimates for submanifolds", Ann. Sci. Ecol. Norm. Sup, 11, pp.451~470 (1978)
- S.-H. Paeng, "A sphere theorem under a curvature perturbation II", Kyushu J. Math, 52, pp.439~454 (1998)
- P. Petersen, "Comparison geometry with integral curvature bounds", Geom. Funct. Anal, 7, pp.1011~1030 (1997)
- J.-G. Yun, "Mean curvature comparison with L1-norms of Ricci curvature", Canad. Math. Bull, 49(1), pp.152~160 (2006)
- D. Yang, "Convergence of Riemannain manifolds with Integral bounds on curvature I", Ann. Sci. Ecol. Norm. Sup, 25, pp.77~105 (1992)
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