On collapsing of Alexandrov spaces and geometry of metric currents
| Project/Area Number |
15K17529
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Fukuoka University (2017-2018)
Gakushuin University (2016)
Tohoku University (2015) |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2015-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Keywords | アレクサンドロフ空間 / グロモフ・ハウスドルフ収束 / 崩壊理論 / 距離カレント / 崩壊 / Delzant 多面体 / 閉凸体 / リプシッツ・ホモトピー / 鈍角定数 / 良い被覆 / リプシッツ構造 |
|---|
| Outline of Final Research Achievements |
We were going to study topological/geometric structures of Alexandrov spaces via phenomena of convergence of spaces. Here, convergences are divided into two cases called collapsing and non-collapsing, which are important.
In our study, we obtained a kind of stability of Lipschitz homotopy structure of Alexandrov space in non-collapsing case, and classified the topology of collapsing 3-dimensional Alexandrov spaces with boundary. We have put the former results together in several papers. The latter is on going.
|
| Academic Significance and Societal Importance of the Research Achievements |
曲率が下に有界なリーマン多様体の構造を調べる際に, アレクサンドロフ空間という対象が自然に現れます. アレクサンドロフ空間の適切なモジュライ(空間を要素とする空間)は, グロモフ・ハウスドロフ収束の観点からコンパクトです. コンパクト性は収束列が沢山存在する事を保証します. 我々はアレクサンドロフ空間の収束現象からアレクサンドロフ空間の構造を解明する事に従事しました. 研究成果で述べた事から, アレクサンドロフ空間について, 少しずつですが, その構造を理解する事ができてきています. これらは非常に興味深く今後とも継続してやるべき研究であると考えています.
|
Report
(5 results)
Research Products
(33 results)
