| Project/Area Number |
15K17546
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Omori Toshiaki 東京理科大学, 理工学部数学科, 助教 (20638225)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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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| Keywords | 指数調和写像 / 調和写像 / 離散曲面 / グラフスペクトル / 同変写像 / Liouville性 / 指数調和写像流 / 球面ホモトピー群 |
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| Outline of Final Research Achievements |
Several existence theorems for exponentially harmonic maps are obtained. More precisely, an existence theorem for exponentially harmonic maps in the case that the source manifold is noncompact, and a Liouville-type theorem is also obtained for exponentially harmonic maps with bounded energy whose target has nonpositive curvature. The existence of a time-global solution to a time evolutional equation for exponentially harmonic maps into nonpositively curved manifolds has been proved. Moreover, the existence of a kind of equivariant exponentially harmonic maps between spheres has been proved under without any conditions.
Also, from a viewpoint of the area of material science, some realizations of graphs in the Euclidean space, a discrete surface theory for them, and a continuous limit of their subdivisions are studied. Spectral problems of the Goldberg-Coxeter subdivisions for 3- and 4-valent finite graphs are also studied.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は，これまでのリーマン多様体間の調和写像の存在理論に対して，指数調和写像を用いるという新しい手法により，統一的な理論の理解を与えたという点において価値がある。
また，連続曲面の離散化でもなく，必ずしも面の存在を仮定しない次数3の空間グラフに対して離 散曲面論を構築した。この研究は，既存の曲面論の枠にはまらない非多面体曲面を対象にする という点で新しいものである。
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