Ricci curvature and convergence of Lipschitz functions
Ricci curvature and convergence of Lipschitz functions
复制标题
DOI：
10.4310/cag.2011.v19.n1.a4
复制
发表时间：
2010-05
影响因子：
0.7
通讯作者：
Shouhei Honda
中科院分区：
文献类型：
--
作者：
Shouhei Honda
给出了Lipschitz函数对实测Gromov-Hausdorff拓扑的微分收敛性的一个定义。作为它们的应用，我们给出了非负Ricci曲率流形渐近锥上具有多项式增长的调和函数和欧几里得体积增长的刻画，以及黎曼流形极限空间上的分布拉普拉斯比较定理。
We give a definition of convergence of differential of Lipschitz functions with respect to measured Gromov-Hausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic cones of manifolds with nonnegative Ricci curvature and Euclidean volume growth, and distributional Laplacian comparison theorem on limit spaces of Riemannian manifolds.