Regularity of the first eigenvalue of the p-Laplacian and Yamabe invariant along geometric flows
Regularity of the first eigenvalue of the p-Laplacian and Yamabe invariant along geometric flows
复制标题
DOI：
10.2140/pjm.2011.254.239
复制
发表时间：
2011-12
影响因子：
0.6
通讯作者：
Er-Min Wang;Yu Zheng
中科院分区：
文献类型：
--
作者：
Er-Min Wang;Yu Zheng
我们首先证明了p-Laplace算子的第一特征值和Yamabe不变量在没有曲率假设的弱假设下都是沿着几何流的局部Lipschitz。其次，Yamabe不变量被发现是方向可微的沿着几何流。作为应用，部分回答了Yamabe度规和Einstein度规的一个公开问题。
We first prove that the first eigenvalue of the p-Laplace operator and the Yamabe invariant are both locally Lipschitz along geometric flows under weak assumptions without assumptions on curvature. Secondly, the Yamabe invariant is found to be directionally differentiable along geometric flows. As an application, an open question about the Yamabe metric and Einstein metric is partially answered.