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| 摘要: |
| 本文研究了Cartan-Hadamard流形上带Lorentz范数的Trudinger-Moser不等式. 利用了相关格林函数的逐点估计以及O’Neil不等式, 我们得到了该不等式的最佳常数, 推广了相应欧氏空间上的结果. |
| 关键词: Trudinger-Moser不等式 Lorentz空间 Riemannian流形 负曲率 最佳常数 |
| DOI： |
| 分类号:O177 |
| 基金项目: |
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| TRUDINGER-MOSER INEQUALITIES ON CARTAN-HADAMARD MANIFOLDS UNDER LORENTZ NORMS |
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ZHANG Jia-jie
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| Abstract: |
| The aim of this paper is to study Trudinger-Moser inequalities on a Cartan-Hadamard manifold with Lorentz norm. By using the pointwise estimates of Green's function and O'Neil inequality, we obtain the sharp constants of such inequalities, which generalize the corresponding results in Euclidean spaces. |
| Key words: Trudinger-Moser inequality Lorentz space Riemannian manifold negative curvature sharp constant |
