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 nash inequality nash不等式(3)Nash不等式(3)
 nash不等式
 Nash Inequality and Riemannian Manifold Nash不等式与黎曼流形 短句来源 Nash Inequality on Riemannian Manifold 黎曼流形上的Nash不等式 短句来源 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 Rn. 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． 短句来源
 Nash不等式
 Nash Inequality and Riemannian Manifold Nash不等式与黎曼流形 短句来源 Nash Inequality on Riemannian Manifold 黎曼流形上的Nash不等式 短句来源 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 Rn. 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． 短句来源

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 nash inequality
 By a method of cylindrical symmetrization for the functions belonging to , we give an estimate of the best constant in the trace Nash inequality on . In this paper, we prove that, on Riemannian compact manifolds with boundary, there exists a second constant for trace Nash inequality with its first best constant. This analysis is motivated by the earlier observation that the logarithmic Sobolev inequality controls the Nash inequality. The time decay of the solutions of the degenerate systems is analyzed by means of a generalisation of the Nash inequality. We give geometrical conditions under which there exist extremal functions for the sharp L2-Nash inequality. 更多
 In this paper, we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. We prove that for these processes, transience implies that the semigroups P(t) decay as ||P(t)||1→∞≤Ct-1. Sufficient conditions for general Markov chains are also obtained. 本文得到了生灭过程和一维扩散过程满足Nash不等式的判别准则,并证明 了对此二类过程,非常返性蕴含相应半群如下收敛速度||P(t)||1→∞≤Ct-1.同时也给 出一般马氏链满足Nash不等式的充分条件. 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. 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。 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 Rn. 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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