| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
Let (M,g) be a Riemannian manifold (H＾3, e＾{2f}g_0) (|df| < a < 1/2, f < b), conformal to the 3-dimensional Poincare sphere. Then (M, g) has separation property for surfaces such that absolute value of mean curvature < e＾{－b}(1－2a). Namely, for any placement of finite point set {P_i} on M, there exists a positive number r with following property: For each i, let B_i be a geodesic sphere of radius < r with center P_i and G_i be closed curve in B_i, S be a compact surface such that its boundary is the union ∪_iG_i and its absolute value of mean curvature is less than e＾{－b}(1－2a), then S is contained in the union ∪_iB_i.
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