2015 Fiscal Year Final Research Report
Maximizers of Poisson's integral and the shape of a body
| Project/Area Number |
26887041
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | University of Miyazaki (2015)
Waseda University (2014) |
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Principal Investigator |
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| Project Period (FY) |
2014-08-29 – 2016-03-31
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| Keywords | 中心 / 体 / Poisson積分 / Rieszポテンシャル |
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| Outline of Final Research Achievements |
For a body (the closure of a bounded open set) in Euclidean space, we investigated a maximizer of the potential obtained as the convolution of a radially symmetric function and the characteristic function of the body. It is known that a maximizer of the potential defines a center of the body. The location and number of centers were studied. Concretely, centers defined by Poisson’s integral or by the Riesz potential were studied. In general, such centers depend on parameters. A necessary and sufficient condition for the existence of a stationary center was given. It was shown that every convex body has a unique center defined by Poisson’s integral. A sufficient condition for the uniqueness of a center defined by the Riesz potential was given.
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| Free Research Field |
凸幾何学
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