2013 Fiscal Year Final Research Report
Geometry of analytic singularities
| Project/Area Number |
23540087
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hyogo University of Teacher Education |
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Principal Investigator |
KOIKE SATOSHI 兵庫教育大学, 学校教育研究科(研究院), 教授 (60161832)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKUI Toshizumi 埼玉大学, 大学院・理工学研究科, 教授 (90218892)
SHIOTA Masahiro 名古屋大学, 大学院・多元数理科学研究科, 名誉教授 (00027385)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 点列選択性性質 / A'Campo 曲率隆起 / 曲率集中化 / ツリーモデル |
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| Research Abstract |
Analytic singularity, in general, can be considerd as a singular point of an analytic set or a singular point of an analytic function. In this research we discussed the both cases, and obtained the following results.
In the first case we laid the basis for the geometry of sets satisfying the Sequence Selection Property whose notion had been introduced by L. Paunescu of University of Sydney and me. In particular, we showed Sequence Selection Property Preserving Theorem and Transversality Preserving Theorem at a singular point of a set,
On the other hand, in the latter case, we formulated a condition for the appearance of A'Campo curvature bumps in a family of level curves of a two variable analytic function around a singular point of the function. In addition, we gave a condition for the appearance of concentration of curvature in the family pf level curves, using the tree model of the function.
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Research Products
(20 results)
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[Remarks] Satoshi Koike, Tzee-Char Kuo and Laurentiu Paunescu, A'Campo curvature bumps and the Dirac phenomenon near a singular point, arXiv:1206, 0525
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[Remarks] Satoshi Koike and Laurentiu Paunescu, On the geometry of sets satisfying the sequence selection property, arXiv: 1201.1669 (雑誌論文○6 ).
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[Remarks] Satoshi Koike, Tzee-Char Kuo and Laurentiu Paunescu, Non concentrtion of curvature near singular points of two variable analytic functions, (雑誌論文○5 ).
