The geometry of Radon-Nikodym Lipschitz differentiability spaces
The geometry of Radon-Nikodym Lipschitz differentiability spaces
复制标题
Radon-Nikodym Lipschitz 可微空间的几何
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Sean Li
中科院分区：
文献类型：
--
作者：
David Bate;Sean Li
利用Alberti表示在度量测度空间中引入了连通点的概念，并证明了它等价于满足Cheeger关于Lipschitz映射到Banach空间的可微性理论的空间，且具有Radon-Nikodym性质.然后，我们证明，这也是等价于满足一个渐近非齐次庞加莱不等式。最后，在取Gromov-Hausdorff切线的条件下，将这个非齐次Poincar 'e不等式改进为一个非渐近形式，并利用这个改进形式导出了切线的拟凸性.
We introduce a notion of connecting points in a metric measure space by Alberti representations and show that it is equivalent to the space satisfying the differentiability theory of Cheeger for Lipschitz maps into Banach spaces with the Radon-Nikodym property. We then prove that this is also equivalent to satisfying an asymptotic non-homogeneous Poincar\'e inequality. Finally we show that this non-homogeneous Poincar\'e inequality is improved to a non-asymptotic version under taking Gromov-Hausdorff tangents and use this improved form to derive quasiconvexity of the tangents.