Geometric inequalities for manifolds with Ricci curvature in the Kato class
Geometric inequalities for manifolds with Ricci curvature in the Kato class
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DOI：
10.5802/aif.3346
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发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
G. Carron
中科院分区：
文献类型：
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作者：
G. Carron
对于满足Euclidean Sobolev不等式和Ricci曲率谱型条件的完备黎曼流形，我们得到了一个Euclidean体积增长的结果。对于Ricci曲率控制在Kato类中的闭流形，我们也得到了特征值估计、热核估计、Betti数估计。
We obtain an Euclidean volume growth results for complete Riemannian manifolds satisfying a Euclidean Sobolev inequality and a spectral type condition on the Ricci curvature. We also obtain eigenvalue estimates, heat kernel estimates, Betti number estimates for closed manifolds whose Ricci curvature is controlled in the Kato class.