| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
(1) Any critical point of a potential with kernel being a monotone function of the distance is included in a minimal unfolded region. Some geometric properties of the minimal unfolded regions have been given. (2) Regularization of the Riesz potential and Riesz energy of a submanifold of the Euclidean space is given. Some of the residues of the Riesz energy thus obtained of a compact body have been computed (joint work with Gil Solanes). (3) A program for the optimal art-gallery problem, which seeks for an optimal position of cameras to monitor a given gallery, has been obtained via outsourcing. (4) A program that can deform a given knot in the unit 3-sphere to decrease the energy has been obtained by outsourcing to Wolfram.
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