Study on hypersurfaces of constant anisotropic mean curvature with singulalities

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610016
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyushu University
• Principal Investigator: KOISO Miyuki 九州大学, マス・フォア・インダストリ研究所, 教授 (10178189)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 非等方的エネルギー / ウルフ図形 / 平均曲率一定曲面 / 変分問題 / ローレンツ・ミンコフスキー空間 / ローレンツ多様体 / 離散曲線 / 離散捩率

Outline of Final Research Achievements

We studied a mathematical model of small crystals. They are equilibrium surfaces of an anisotropic surface energy which is the integral of the surface tension over the surface. The surface tension depends on the direction of each point of the surface. We derived the condition for a surface to be an equilibrium surface, and we proved the uniqueness of the local energy minimizer for closed plane curves. We also studied a mathematical model of small double crystals, surfaces with constant mean curvature in Lorenz spaces, and curvatures of discrete space curves.

Free Research Field

微分幾何学