HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE
HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE
复制标题
DOI：
10.1142/s0219199713500430
复制
发表时间：
2014-04
影响因子：
1.6
通讯作者：
Qiaohua Yang;Dan Su;Yinying Kong
中科院分区：
文献类型：
--
作者：
Qiaohua Yang;Dan Su;Yinying Kong
设M是完备的单连通的负曲率黎曼流形.得到了M上与测地距离有关的哈代和Rellich不等式的锐常数.进一步，当M具有严格负曲率时，我们证明了Lp哈代不等式可以通过在p ≥ 2的情形下增加类似Brezis-Vazquez改进的余项而得到全局加细，这与欧氏空间的情形相反.
Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain the sharp constants of Hardy and Rellich inequalities related to the geodesic distance on M. Furthermore, if M is with strictly negative curvature, we show that the Lp Hardy inequalities can be globally refined by adding remainder terms like the Brezis–Vazquez improvement in case p ≥ 2, which is contrary to the case of Euclidean spaces.