| Project/Area Number |
18H01125
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 12010:Basic analysis-related
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
新井 仁之 早稲田大学, 教育・総合科学学術院, 教授 (10175953)
須川 敏幸 東北大学, 情報科学研究科, 教授 (30235858)
佐官 謙一 大阪公立大学, 数学研究所, 特別研究員 (70110856)
小森 洋平 早稲田大学, 教育・総合科学学術院, 教授 (70264794)
柳下 剛広 山口大学, 大学院創成科学研究科, 講師 (60781333)
|
|---|
| Project Period (FY) |
2018-04-01 – 2023-03-31
|
| Project Status |
Completed (Fiscal Year 2023)
|
| Budget Amount *help |
¥13,780,000 (Direct Cost: ¥10,600,000、Indirect Cost: ¥3,180,000)
Fiscal Year 2022: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2021: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2020: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2018: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
|
|---|
| Keywords | 複素解析 / 実解析 / 調和解析 / 双曲幾何 / 複素解析学 |
|---|
| Outline of Final Research Achievements |
The Teichmueller space has long been studied in various fields of mathematics as a deformation space of Riemann surfaces. In the study of the universal Teichmueller space, which provides the foundation for complex analytic theory, it has been found that assuming absolute continuity as the regularity in the mappings enriches the content of the analysis. This research project has integrated harmonic analytic theories of BMO spaces and Besov spaces into the theory of Teichmueller spaces. By doing so, it has developed the theory of Teichmueller spaces of function spaces through the mutual complementarity of complex analysis and real analysis. In particular, it has established the foundation for the complex analytic deformation theory of families of curves, such as quasicircles and Weil-Petersson curves, instead of Riemann surfaces, by parametrizing them within the corresponding Teichmueller spaces.
|
| Academic Significance and Societal Importance of the Research Achievements |
タイヒミュラー空間の複素解析的研究は，学術的にはリーマン面や曲線の変形理論の理解を深め，代数幾何学，力学系理論，数理物理学など多くの分野での基礎理論を強化する．この研究は古典的な調和解析の理論を融合し，複素解析と実解析の相互補完を図ることができる．社会的には，これらの理論的進展は画像処理，自然現象のモデル化など，精密な幾何学的・解析的枠組みを必要とする分野に貢献する．タイヒミュラー空間の理解が深まることで，これらの応用領域における新たな革新が促進されることから理論数学と実践的応用の両面で広範な影響をもたらす．
|
