| 黎曼流形上的Nash不等式 |
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| 引用本文： | 阮其华,陈志华. 黎曼流形上的Nash不等式[J]. 数学学报, 2006, 49(4): 915-918. DOI: cnki:ISSN:0583-1431.0.2006-04-023 |
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| 作者姓名： | 阮其华 陈志华 |
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| 作者单位： | [1]中山大学数学与计算科学学院,广州510275 [2]福建省莆田学院数学系,莆田351100 [3]同济大学数学与应用数学系,上海200092 |
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| 基金项目： | 国家自然科学基金资助项目（10271089）;福建省教育厅资助项目（JA04266） |
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| 摘 要： | 本文通过对满足Nash不等式的黎曼流形的研究,证明了对任一完备的Ricci曲率非负的n维黎曼流形,若它满足Nash不等式,且Nash常数大于最佳Nash常数,则它微分同胚于Rn．
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| 关 键 词： | Ricci曲率 Nash不等式 微分同胚 |
| 文章编号： | 0583-1431（2006）04-0915-04 |
| 收稿时间： | 2004-12-08 |
| 修稿时间： | 2004-12-082005-04-11 |
Nash Inequality on Riemannian Manifold |
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| Qi Hua RUAN Zhi Hua CHEN. Nash Inequality on Riemannian Manifold[J]. Acta Mathematica Sinica, 2006, 49(4): 915-918. DOI: cnki:ISSN:0583-1431.0.2006-04-023 |
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| Authors: | Qi Hua RUAN Zhi Hua CHEN |
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| Affiliation: | Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China ; Department of Mathematics, Putian University, Putian 351100, P. R. China;Department of Mathematics, Tongji University, Shanghai 200092, P. R. China |
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| Abstract: | In this paper, we study the property of Riemannian manifold satisfying Nash inequality, and prove that for any complete n-dimensional Riemannian manifold with nonnegative Ricci curvature, if the Nash inequality is satisfied and the Nash constant is more than the best Nash constant, then the manifold is diffeomorphic to R^n. |
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| Keywords: | Ricci curvature Nash inequality diffeomorphic |
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