论文标题
在标量和RICCI曲率上
On Scalar and Ricci Curvatures
论文作者
论文摘要
本报告的目的是承认格罗莫夫先生对几何形状的影响对我们自己的作品的影响。这是两个方面：在第一部分中，我们旨在描述一个问题3中的某些结果：哪个开放的3个manifolds具有完整的riemannian指标，即正面或非负标量曲率？在第二部分中，我们在非一定是平滑的度量测量空间上寻找“ RICCI曲率下限”概念的弱形式。我们描述了最新结果，其中一些已经发布在[Arxiv：1712.08386]中，我们建议在其中使用卷熵。我们还尝试使用Bishop-Gromov的不等式提供下面的RICCI曲率的新合成版本。
The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature? In the second part we look for weak forms of the notion of "lower bounds of the Ricci curvature" on non necessarily smooth metric measure spaces. We describe recent results some of which are already posted in [arXiv:1712.08386] where we proposed to use the volume entropy. We also attempt to give a new synthetic version of Ricci curvature bounded below using Bishop-Gromov's inequality.
