2010 Fiscal Year Final Research Report
Canonical Riemannian metrics on simplicial complexes
| Project/Area Number |
20540201
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Tohoku University |
|---|
Principal Investigator |
YAMADA Sumio Tohoku University, 大学院・理学研究科, 准教授 (90396416)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
OBITSU Kunio 鹿児島大学, 理工学研究科, 准教授 (00325763)
KIDA Yoshikata 京都大学, 大学院・理学研究科, 准教授 (90451517)
SHIROMIZU Tetsuya 京都大学, 大学院・理学研究科, 准教授 (10282716)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Keywords | 調和写像 / リーマン面 / モジュライ空間 / コクセター複体 / 極小曲面 / 一般相対性理論 / 実解析性 |
|---|
| Research Abstract |
We have demonstrated the importance of boundary geometry of various Riemannian metrics when the boundary components act as facets where simplices meet within a simplicial complex, in terms of its effect on the global geometric structures of the simplicial complex. This has been observed and investigated in the contexts of Weil-Petersson geometry of Teichmuller spaces, singular minimal surface theory arising in Geometric Measure Theory, and the geometry of event horizons within Einstein manifolds.
|
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
[Remarks] 山田澄生,時計仕掛けの地図-ポアンカレと相対性理論-, 数理科学10特集ポアンカレ,2008年,44-50.
