Geodesic
Volume comparison theorems for manifolds with radial curvature bounded
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 71-86 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume comparisons are made between annulus or geodesic balls on the original manifold and those on the model space.
In this paper, for complete Riemannian manifolds with radial Ricci or sectional curvature bounded from below or above, respectively, with respect to some point, we prove several volume comparison theorems, which can be seen as extensions of already existing results. In fact, under this radial curvature assumption, the model space is the spherically symmetric manifold, which is also called the generalized space form, determined by the bound of the radial curvature, and moreover, volume comparisons are made between annulus or geodesic balls on the original manifold and those on the model space.
DOI : 10.1007/s10587-016-0240-7
Classification : 52A38, 53C20, 53C21
Keywords: spherically symmetric manifolds; radial Ricci curvature; radial sectional curvature; volume comparison 
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Mao, Jing. Volume comparison theorems for manifolds with radial curvature bounded. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 71-86. doi: 10.1007/s10587-016-0240-7

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