Geometric study of potentials and optimal art gallery problem
| Project/Area Number |
25610014
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Chiba University (2015-2016)
Tokyo Metropolitan University (2013-2014) |
|---|
Principal Investigator |
Imai Jun 千葉大学, 大学院理学研究科, 教授 (70221132)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
HAMADA TATSUYOSHI 日本大学, 生物資源学部, 准教授 (90299537)
|
|---|
| Project Period (FY) |
2013-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| 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)
|
|---|
| Keywords | Riesz ポテンシャル / 美術館問題 / プログラミング / 正則化 / ポテンシャル / 結び目のエネルギー / 幾何 / 最適化 / min-max / ポテンシャル論 / 凸幾何学 / 国際研究者交流 |
|---|
| 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.
|
Report
(5 results)
Research Products
(15 results)
