2017 Fiscal Year Final Research Report
Development of geometric analysis of singular collapsing phenomenon
| Project/Area Number |
15K13436
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Research Collaborator |
NAGANO Koichi (30333777)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | CAT(1)空間 / 特異空間 / 線識面 |
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| Outline of Final Research Achievements |
I have investigated ruled surfaces in two-dimensional CAT(1)-spaces, which is a key to the determination of the local structure of such spaces. I have succeeded in proving that a ruled surface in a small region around a given point of a two-dimensional CAT(1)-space is a CAT(1)-space for the interior metric, and that it is homeomorphic to a two-disk. Based on this result, I would like to determine the local structure of such a space as a gluing of finitely many CAT(1)-Lipschitz disks, in the near future.
I have introduced the notion of asymptotic self-similar sets, and determined their Hausdorff dimensions. As an application, I have determined the Hausdorff dimension of Sierpinski gaskets on surfaces.
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| Free Research Field |
微分幾何学
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