The local structure and topological structure on metric measure spaces

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17541
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kumamoto University (2016-2017); Kyoto University (2015)
• Principal Investigator: Kitabeppu Yu 熊本大学, 大学院先端科学研究部(理), 准教授 (50728350)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: RCD 空間 / 正則集合 / Gromov-Hausdorff 収束

Outline of Final Research Achievements

RCD spaces are one of the generalization of Riemannian manifolds with lower Ricci bound and upper dimension bound. These spaces are known to be worth studying in order to understanding the geometry of Riemannian manifolds. However it is difficult to analyze such spaces because of the complexity of local structure in those. In our study, we classify the low dimensional RCD spaces. And we define the subclass of RCD spaces that can be treated easier than generic ones. Also, we prove the high dimensional regular sets exist plentifully.

Free Research Field

リーマン幾何学