non-existence of minimal surfaces connecting distant curves

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654026
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Osaka University
• Principal Investigator: KOISO Norihito 大阪大学, 理学(系)研究科(研究院), 教授 (70116028)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 極小部分多様体 / 平均曲率一定曲面

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.

Free Research Field

微分幾何学