| Nash不等式与黎曼流形 |
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| 引用本文： | 阮其华. Nash不等式与黎曼流形[J]. 莆田学院学报, 2005, 12(2): 9-10,35 |
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| 作者姓名： | 阮其华 |
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| 作者单位： | 莆田学院,数学系,福建,莆田,351100 |
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| 基金项目： | 福建省教育厅基金资助课题(JA04266) |
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| 摘 要： | 运用光滑截断函数的性质,证明了对任一n维完备的黎曼流形,若它的Ricci曲率非负,且满足一个Nash不等式,则它微分同胚于Rn。另外,利用迭代的方法,得到了在没有曲率假设下,若黎曼流形满足Nash不等式,则测地球的体积具有极大增长。
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| 关 键 词： | Nash不等式 微分同胚 黎曼流形 |
| 文章编号： | 1672-4143(2005)02-0009-02 |
Nash Inequality and Riemannian Manifold |
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| RUAN Qi-hua. Nash Inequality and Riemannian Manifold[J]. journal of putian university, 2005, 12(2): 9-10,35 |
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| Authors: | RUAN Qi-hua |
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| Abstract: | In this paper, we use the property of the smooth cut-off function to prove the following result: for any n-dimensional complete Riemannian manifold with nonnegative Ricci curvature, if one of the Nash inequalities is satisfied, then it is diffeomorphic to Rn . We also use the iterating method to obtain that if the Nash inequalities are satisfied on the Riemannian manifold without any curvature assumption, then the geodesic ball has maximal volume growth. |
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| Keywords: | Nash inequalities diffeomorphic Riemannian manifold |
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