| Project/Area Number |
18H03670
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Review Section |
Medium-sized Section 12:Analysis, applied mathematics, and related fields
|
|---|
| Research Institution | Tokyo Institute of Technology |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
高坂 良史 神戸大学, 海事科学研究科, 教授 (00360967)
石井 克幸 神戸大学, 海事科学研究科, 教授 (40232227)
三浦 達哉 東京工業大学, 理学院, 准教授 (40838744)
高棹 圭介 京都大学, 理学研究科, 准教授 (50734472)
可香谷 隆 室蘭工業大学, 大学院工学研究科, 准教授 (60814431)
小野寺 有紹 東京工業大学, 理学院, 准教授 (70614999)
|
|---|
| Project Period (FY) |
2018-04-01 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2022)
|
| Budget Amount *help |
¥42,770,000 (Direct Cost: ¥32,900,000、Indirect Cost: ¥9,870,000)
Fiscal Year 2022: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000)
Fiscal Year 2021: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2020: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2019: ¥9,360,000 (Direct Cost: ¥7,200,000、Indirect Cost: ¥2,160,000)
Fiscal Year 2018: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
|
|---|
| Keywords | 平均曲率流 / 変分問題 / 極小曲面 / 幾何学的測度論 / 特異点 / 正則性 / Mean curvature flow / Calculus of variations / Geometric measure theory / Minimal surface / Geometric analysis / mean curvature flow / calculus of variations / geometric measure theory / minimal surface / geometric analysis |
|---|
| Outline of Final Research Achievements |
In the field of geometric analysis, minimal surface is historically an important object of study and mean curvature flow which is the time-evolutionary version gives a dynamic perspective to the minimal surfaces. For Brakke flow which is a mean curvature flow considered within the framework of geometric measure theory, we proved the following: the time-global existence theorem with fixed boundary condition, the existence of canonical mean curvature flow whose concept is new, an ultimate end-time regularity theorem, and an existence theorem of non-trivial Brakke flow starting from minimal surface with flat singularity. The last result naturally leads to a new concept of dynamic stability/instability for minimal surfaces with singularities.
|
| Academic Significance and Societal Importance of the Research Achievements |
幾何学的測度論を用いた極小曲面に関する結果は決定的で学術的に重要なものが多い一方で、その時間発展版であるBrakke流については未知の部分が多い。当該研究はその基本的な存在定理や正則性定理などに関して着実な結果を出し、またそれらを通じて標準的平均曲率流や極小曲面の動的な安定性など、複数の新しい概念の創出に至っているという点で学術的意義がある。
|
