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皇冠428428娱乐娱城:2023年冬短期课程-Quantitative Maximal Rigidity of Ricci Curvature Bounded Below

皇冠428428娱乐娱城

2023年冬短期课程:

Quantitative Maximal Rigidity of Ricci Curvature Bounded Below

戎小春教授(皇冠428428娱乐娱城)

A goal of this mini-course is to give a quick introduction to an on-going research area (in the title) in Metric Riemannian geometry.

In Riemannian geometry, a maximal rigidity on an n-manifold M of Ricci curvature bounded below by (n?1)H is a statement that a geometric or a topological quantity of M is bounded above by that of an n-manifold of constant sectional curvature H, and “=” implies that M has constant sectional curvature H.

A quantitative maximal rigidity of Ricci curvature bounded below is a statement that if a geometric quantity is almost maximal, then M admits a nearby metric of constant sectional curvature H (which may require additional conditions). Indeed, the Cheeger-Colding-Naber theory on Ricci limit spaces initiated in establishing a quantitative maximal volume rigidity of positive Ricci curvature.

CONTENTS

1. Maximal rigidities of Ricci curvature bounded below

2. Gromov-Hausdorff topology, and Ricci limit spaces

3. Quantitative maximal rigidities of Ricci curvature bounded below

4. Structures on a Ricci limit space of a collapsing sequence with local Ricci bounded covering geometry

时间:周一三五上午9:30-11:30(除假期时间),共大约九次左右;第一次上课时间2023-12-29周五上午

地点:校本部教二楼 627教室 

欢迎研究生同学参加!

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