| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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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