2013 Fiscal Year Final Research Report
Study of convergence and collapsing phenomena by methods of geometric analysis
| Project/Area Number |
21340013
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SHIOYA Takashi 東北大学, 大学院・理学研究科, 教授 (90235507)
ISOZAKI Hiroshi 筑波大学, 数理物質系, 教授 (90111913)
NAGANO Koichi 筑波大学, 数理物質系, 講師 (30333777)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 崩壊理論 / グロモフ・ハウスドルフ収束 / スペクトル逆問題 / アレクサンドロフ空間 / 幾何解析 / 測度距離空間 |
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| Research Abstract |
We obtained the uniqueness and the stability of the inverse spectral problem
concerning the local data of the heat kernels in the moduli of closed Rimennian manifolds whose sectional curvature and diameters are uniformly bounded (T.Yamaguchi, S. Kurylev, M.Lassas). We classified the collapsing phenomena of three-dimensional closed Alexandrov spaces with cuvature uniformly bounded below. Moreover we proved the local strong Lipschitz contractibility of Alexandrov spaces and the stability of strongly Lipschitz contractible balls(T.Yamaguchi, A.Mitsuishi). We proved that the curvature dimension condition of Ricci curvature is preserved under the concentration of metric measure spaces(T.Shioya, K.Funano). We reconstructed hyperbolic orbifolds from S-matirix corresponding to a general end (H. Isozaki, Y. Kurylev).
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Research Products
(50 results)
