2016 Fiscal Year Final Research Report
New methods on geometric analysis of variational problems for surfaces
Project/Area Number |
25287012
|
Research Category |
Grant-in-Aid for Scientific Research (B)
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Allocation Type | Partial Multi-year Fund |
Section | 一般 |
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)
|
Co-Investigator(Kenkyū-buntansha) |
庄田 敏宏 佐賀大学, 文化教育学部, 准教授 (10432957)
川上 裕 金沢大学, 数物科学系, 准教授 (60532356)
小野寺 有紹 九州大学, マス・フォア・インダストリ研究所, 助教 (70614999)
|
Co-Investigator(Renkei-kenkyūsha) |
CHENG Qing-Ming 福岡大学, 理学部, 教授 (50274577)
MIYAMOTO Umpei 秋田県立大学, 総合科学教育研究センター, 准教授 (70386621)
EJIRI Norio 名城大学, 理工学部, 教授 (80145656)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Keywords | 平均曲率一定曲面 / 極小曲面 / 安定性 / 変分問題 / 分岐理論 / 三重周期極小曲面 / 自由境界問題 / プラトー問題 |
Outline of Final Research Achievements |
Under given boundary conditions, minimal surfaces are critical points of area, and surfaces with constant mean curvature (CMC surfaces) are critical points of area among surfaces enclosing the same volume. Such a surface is said to be stable if it attains a local minimum of area for all admissible variations. In this research, we studied criteria for stability, existence and uniqueness of (stable) critical points, bifurcation of critical points, for fixed, free, and periodic boundary conditions.
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Free Research Field |
微分幾何学
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