| Budget Amount *help |
¥16,250,000 (Direct Cost: ¥12,500,000、Indirect Cost: ¥3,750,000)
Fiscal Year 2022: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2021: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2020: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2019: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2018: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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| Outline of Final Research Achievements |
We consider the Yamabe problem on edge-cone n-spheres (S^n, h_a) with cone angle 2πa. When 0 < a < 1, we have proved that any constant scalar curvature metric in the conformal class [h_a] is the pull-back of h_a
by a conformal transformation of (S^n, [h_1]) keeping the singularities S^{n-2} of h_a. When a ≧ 2, we have proved that there is no edge-cone Yamabe metric in [h_a]. When 1 < a < 2, the Yamabe problem is still unsolvable.
We have obtained some results of the Ricci flow with a suitable boundary condition on compact manifolds with boundary. We have also obtained an Obata-type theorem on compact Einstein manifolds with boundary.
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