论文标题
加倍不平等和关键的迪里奇特征函数
Doubling inequalities and critical sets of Dirichlet eigenfunctions
论文作者
论文摘要
我们研究了边界和紧凑型利曼尼亚歧管内部的dirichlet本征函数的临界集合集的梯度和上限的急剧加倍不平等。大多数努力致力于为梯度获得急剧的加倍不平等。开发了新技术，以克服双流式在平滑歧管中获得双倍不平等的不平等现象的困难。分析riemannian流形中关键集的急剧上限是不平等的后果。
We study the sharp doubling inequalities for the gradients and upper bounds for the critical sets of Dirichlet eigenfunctions on the boundary and in the interior of compact Riemannian manifolds. Most efforts are devoted to obtaining the sharp doubling inequalities for the gradients. New technique is developed to overcome the difficulties on the unavailability of the double manifold in obtaining doubling inequalities in smooth manifolds. The sharp upper bounds of critical sets in analytic Riemannian manifolds are consequences of the doubling inequalities.
