The generalized rotational hypersurfaces and their geomteric evolution problems

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400156
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Saitama University
• Principal Investigator: NAGASAWA Takeyuki 埼玉大学, 理工学研究科, 教授 (70202223)
• Co-Investigator(Renkei-kenkyūsha): TACHIKAWA Atsusi 東京理科大学, 理工学部, 教授 (50188257) ; YAZAKI Shigetoshi 明治大学, 理工学部, 教授 (00323874) ; KOHSAKA Yoshihito 神戸大学, 大学院海事科学研究科, 准教授 (00360967)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 一般化された回転超曲面 / メビウス・エネルギー / メビウス不変性 / 変分公式 / 変分問題

Outline of Final Research Achievements

When we deal with variational problems for hypersurfaces, some difficulties may occur.　　Assuming some symmetry, the problems can be reduced to the problem of curves.　　Here we obtain three kind of results.　　First, we reduce the inelastic collision of elastic shell to the problem of centerline, and propose a mathematical model and perform numerical simulation. Secondly, we study the global existence of rotational hypersurface with prescribed mean curvature. The problem can be reduced to the global existence of solutions of an ordinary differential equation which the generating curve satisfies. We resolve the problem completely for all types of hypersurfaces. Lastly we deal with the Moebius energy. We show that the energy can be decomposed into three parts keeping the Moebius invariance. By ude of the decomposition. the variational formulas are derived explicitly. Furthermore we have their estimates on several function spaces.

Free Research Field

非線型解析