Volume comparison theorems for manifolds with radial curvature bounded

Jing Mao

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 1, page 71-86
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mao, Jing. "Volume comparison theorems for manifolds with radial curvature bounded." Czechoslovak Mathematical Journal 66.1 (2016): 71-86. <http://eudml.org/doc/276782>.

@article{Mao2016,
abstract = {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.},
author = {Mao, Jing},
journal = {Czechoslovak Mathematical Journal},
keywords = {spherically symmetric manifolds; radial Ricci curvature; radial sectional curvature; volume comparison},
language = {eng},
number = {1},
pages = {71-86},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Volume comparison theorems for manifolds with radial curvature bounded},
url = {http://eudml.org/doc/276782},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Mao, Jing
TI - Volume comparison theorems for manifolds with radial curvature bounded
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 71
EP - 86
AB - 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.
LA - eng
KW - spherically symmetric manifolds; radial Ricci curvature; radial sectional curvature; volume comparison
UR - http://eudml.org/doc/276782
ER -

References

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