An advanced study of cut locus and related topics
| Project/Area Number |
26400072
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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 | Kumamoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
清原 一吉 岡山大学, 自然科学研究科, 教授 (80153245)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 測地線 / 最小跡 / 共役跡 / 多面体 / 第一共役跡 / 全曲率 / 全捩率 |
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| Outline of Final Research Achievements |
This research of cut locus was separated 5 themaes and developed all themaes synthetically. (A) As an extension of Jacobi's last statement in general dimension, we finished the paper and submitted it. As a thread construction of quadric surface, we published the paper. (B) A main paper of series of studies of the structure of cut locus by using graph theory was published. (C) We almost finished the paper of the relation between the number of distance functions such that a point is critical and the topology of orientable surface. (D) We discussed continuous flattening of non-convex polyhedral surface by using cut locus, but we firstly got the result by the other method. (E) We published the paper constructing the Finslerian metric with fractal cut locus.
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Report
(4 results)
Research Products
(62 results)
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[Journal Article] Thread construction revisited2016
Author(s)
Jin-ichi Itoh, Kazuyoshi Kiyohara
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Journal Title
Journal of the Mathematical Society of Japan
Volume: 68
Issue: 3
Pages: 917-938
DOI
NAID
ISSN
0025-5645, 1881-1167, 1881-2333
Related Report
Peer Reviewed / Open Access
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[Journal Article] Continuous flattening of orthogonal polyhedra2016
Author(s)
Erik Demaine, Martin Demaine, Jin-ichi Itoh, Chie Nara
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Journal Title
Revised Selected Papers of JCDCGG 2015, J. Akiyama et al. (eds.) LNCS, vol. 9943, Springer-Heidelberg
Volume: LNCS, vol. 9943
Pages: 85-93
DOI
ISBN
9783319485317, 9783319485324
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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[Journal Article] Every graph is a cut locus2015
Author(s)
Itoh, Jin-ichi; Vilcu, Costin
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Journal Title
Journal of the Mathematical Society of Japan
Volume: 67
Issue: 3
Pages: 1227-1238
DOI
NAID
ISSN
0025-5645, 1881-1167, 1881-2333
Related Report
Peer Reviewed / Open Access / Int'l Joint Research
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