2002 Fiscal Year Final Research Report Summary
Research on the Regularity of Solutions for Geometric Variational Problems
| Project/Area Number |
12640221
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
TACHIKAWA Atsushi Tokyo University of Science(T.U.S.), Faculty of Science and Technology, Professor, 理工学部, 教授 (50188257)
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| Co-Investigator(Kenkyū-buntansha) |
FURUTANI Kenro T.U.S., Fac. of Sci. and Tech., Professor, 理工学部, 教授 (70112901)
KOBAYASHI Takao T.U.S., Fac. of Sci. and Tech., Professor, 理工学部, 教授 (90178319)
NAGASAWA Takeyuki Saitarna Univ., Fac. of Science, Professor, 理学部, 教授 (70202223)
TANAKA Makiko T.U.S., Fac. of Sci. and Tech., Professor, 理工学部, 助教授 (20255623)
YAMAZAKI Taeko T.U.S., Fac. of Sci. and Tech., Associate Professor, 理工学部, 助教授 (60220315)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Variattional Problems / regularity / Harmonic maps / Finsler manifold / energy functional |
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| Research Abstract |
The variational problems for the energy functional defined for maps between Riemmannian manifolds have been studied by many mathematicians.Namely, about harmonic maps between Riemannian manifolds, we have many deep results.Recently, some generalisations of harmonic maps attract the interest of several reseachers.In this research, we considered some generalised notion of harmonic maps and got some results on their regularity
In the year 2000, we treated harmonic maps with potentials, and got their existence and regularity results.In the year 2001, we considered more generalised notion of harmonic maps so-called F-farmonic tnays and get their existence and partial regularity results
In the year 2002, we treated harmonic maps into Finsler manidolds.Finsler manifolds are natural generalization of Riemannian ones.P.Centore defined the energy of a map between Finsler manifolds.We used Centores definition and specialized it for the case that the source manifold is Eucldean space. We calculated the Euler-Lagrange equation of it and got the equation for hannonic maps from an. Euclidean space R^m to a Finsler manifold. Moreover, we got a partial regularity result for energy minimizing map from R^m to a Finsler manifold for the case that m=3,4.More precisely, we proved that for the above cases the enegy minimizing maps are Wilder continuous outside the singular set whose Hausdorff dimension is less that m-2.
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