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数学进展 - 2018, Vol. 47(1): 95-108
研究论文
凸区域上的$p$-阶特征函数及相关的度量
The $p$-th Characteristic Function and Associated Metric on a Convex Domain

吴亚东
WU Yadong

江西师范大学数学与信息科学学院, 南昌, 江西, 330022
College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi, 330022, P. R. China

出版日期: 2018-01-25
2018, Vol. 47(1): 95-108
DOI: 10.11845/sxjz.2016057b


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摘要 考虑强凸有界区域上的$p$-阶特征函数, 本文给出了它对一类Monge-Ampère方程解的渐近展开式. 另一方面考虑由$p$-阶特征函数定义的一个黎曼度量, 证明了它的截面曲率在边界上趋于$-1$, 且它的曲率张量及各阶共变微分的范数是有界的.
关键词 截面曲率有界几何渐近展开    
Abstract:Considering the $p$-th characteristic function on a strongly convex bounded domain $\Omega$, we give its asymptotic expansion with respect to the solution of Monge-Ampère equation. On the other hand, considering a Riemannian metric defined by the $p$-th characteristic function, we show that its sectional curvatures tend to $-1$ on the boundary $\partial\Omega$, and the norms of its curvature tensors and of all their covariant derivatives are bounded.
Key wordssectional curvature    bounded geometry    asymptotic expansion
PACS:  O186.1  
通讯作者: E-mail: wydmath@163.com   
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