1998 Fiscal Year Final Research Report Summary
Calculus of Variation and Geometric Structures on Manifolds
| Project/Area Number |
09640139
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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 |
Geometry
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| Research Institution | Fukuoka Institute of Technology |
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Principal Investigator |
ITOKAWA Yoe Fukuoka Institute of Technology, Faculty of Information Engineering, Associate Professor., 情報工学部, 助教授 (90223205)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIBATA Shinya Fukuoka Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80279299)
NISHIHARA Masaru Fukuoka Institute of Technology, Faculty of Information Engineering, Professor, 情報工学部, 教授 (20112287)
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| Project Period (FY) |
1997 – 1998
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| Keywords | manifolds / minimal varieties / sectional curvature / Ricci curvature / homology / complex locally convex spaces / systems of P.D.E. / entropy function |
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| Research Abstract |
The head investigator, Yoe Itokawa, in a joint research project with Katsuhiro Shiohama, has shown that complete minimal varieties in complete noncompact manifolds of positive sectional curvature necessarily have unbounded images. The head investigator has obtained some partial results concerning the case where the ambient spaces have only nonnegative curvature, but he is still undecided whether to publish the latter results or wait for further information. In another work, this time with Ryoichi Kobayashi, the head investigator has classified the <planck's constant>-1 -dimensional homology groups of manifolds of nonnegatively Ricci curvature under some relatively weak conditions on the growth rate of their cross-sectional size. The last results were described in the paper"Minimizing currents in open manifolds and <planck's constant>-1 homology of nonnegatively Ricci curved m
The investigator Masaru Nishihara has continued his investigation on the extendability of weakly continuous polynomials on a comples locally convex space E to its bidual space E". He has published his results in the paper "On extensions of holomorphic functions in infinite dimensional spaces" in Proceedings of the Sixth International Colloquium on Complex Analysis.
The investigator Sinya Nishibata has studied systems of coupled hyperbokic and elliptic P.D.E.'s. He was able to prove that the existence of entropy function is equivalent to the simultaneous diagonability of the system and that, under this condition, classical techniques can be used to establish the short-term existence of solutions. In addition, he has also shown that under stability assumptions, long term solutions also exist and when t tends to*, they converge to equilibrium states.
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