Extreme points in non-positive curvature

Developments around positive sectional curvature

This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chronological order.

A Dozen Problems, Questions and Conjectures about Positive Scalar Curvature

We collect a few guesses on possible implications of a lower bound on the scalar curvature of a Riemannian manifold on the size and shape of this manifold.

非负数量曲率下向极端极限空间的几何收敛

Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature

本文研究非负数量曲率流形序列收敛到极端极限空间的问题，证明了序列在保体积内蕴平坦和测度格罗莫夫-豪斯多夫意义下收敛，为检验广义非负数量曲率定义提供了测试空间。

关于具有正数量曲率的完备3-流形中的腰围与宽度不等式

On the waist and width inequality in complete 3-manifolds with positive scalar curvature

本文证明了数量曲率有正下界的完备非紧3-流形上存在由面积和直径受控的曲面构成的奇异叶状结构，从而给出腰围与宽度不等式。

Oberwolfach研讨会报告：正数量曲率度量的分析、几何与拓扑：非负数量曲率流形序列及其他假设的极限

Oberwolfach Workshop Report: Analysis, Geometry and Topology of Positive Scalar Curvature Metrcs: Limits of sequences of manifolds with nonnegative scalar curvature and other hypotheses

本报告综述了非负数量曲率流形序列的示例，宣布了一篇证明极端示例GH和SWIF收敛性的论文，并提出了六个公开问题。

Waist inequality for 3-manifolds with positive scalar curvature

We construct singular foliations of compact three-manifolds $(M^3,h)$ with scalar curvature $R_h\geq Λ_0>0$ by surfaces of controlled area, diameter and genus. This extends Urysohn and waist inequalities of Gromov-Lawson and Marques-Neves.