| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
Let M be an m-dimensional compact submanifold of an n-dimensional Euclidean space. Let B(z) be the integral of the distance between a pair of points x and y in M to the power z over the product space M times M. Consider B(z) as a function of a complex variable z. By a meromorphic regularization, i.e. the regularization via analytic continuation we obtain a meromorphic function with simple poles, called Brylinski beta function of M. If M is an odd dimensional closed submanifold or an even dimensional compact body (closure of an open set of the Euclidean space) then the value of B(z) with z being equal to -2m is invariant under Mobius transformations. This result was obtained in the joint work with Gil Solanes.
We obtain regularized self-inductance of a current in a single loop by applying our method to Neumann formula and Weber formula for mutual inductances. We also studied Mobius invariant metrics on the space of knots.
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