A volume comparison estimate with radially symmetric Ricci curvature lower bound and its applications.
Hu, Zisheng, Jin, Yadong, Xu, Senlin (2010)
International Journal of Mathematics and Mathematical Sciences
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Hu, Zisheng, Jin, Yadong, Xu, Senlin (2010)
International Journal of Mathematics and Mathematical Sciences
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Bernig, Andreas (2003)
Advances in Geometry
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Paweł Grzegorz Walczak (1984)
Annales Polonici Mathematici
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Guangyue Huang, Fanqi Zeng (2016)
Studia Mathematica
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We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.
Jing Mao (2016)
Czechoslovak Mathematical Journal
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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...
Isaac Chavel, Edgar A. Feldman (1974)
Compositio Mathematica
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Luis Guijarro, Peter Petersen (1997)
Annales scientifiques de l'École Normale Supérieure
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Bernig, Andreas (2002)
Advances in Geometry
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Najoua Gamara, Abdelhalim Hasnaoui, Akrem Makni (2015)
Open Mathematics
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In this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds. We also prove an isoperimetric inequality for the torsional ridigity of such domains