2012 Fiscal Year Final Research Report
Study of nonlinear geometric problems by methods of algebraic analysis
| Project/Area Number |
23654047
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KATAOKA Kiyoomi 東京大学, 大学院・数理科学研究科, 教授 (60107688)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 関数方程式 |
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| Research Abstract |
We succeeded in describing the surfaces in R^3 which include several continuous families of circles completely by some systems of nonlinear partial differential equations of order 5. We gave explicitly the very complicated form of this system of equations. Further, as applications, we obtained an upper estimate of the number of parameters classifying those surfaces, and a reduction of this system to a finite system of algebraic ordinary differential equations for 5 unknown functions of one variable.
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