2023 Fiscal Year Final Research Report
Collapsing theory of Alexandrov spaces and geometric analysis
| Project/Area Number |
20K03598
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Fukuoka University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | アレクサンドロフ空間 / リプシッツ・ホモトピー / 崩壊 / ピラミッド / 測度集中 |
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| Outline of Final Research Achievements |
We study non-collpasing Alexandrov spaces and their stability in the point of view of quantitative Lipschitz homotopy convergence (with T. Fujioka and T. Yamaguchi). Furthermore, I and Yamaguchi write a paper about collapsing 3-dimensional Alexandrov spaces with boundary. H. Fujita, Y. Kitabeppu and I study a convergence theory of Delzant construction with respect to Guillemin metric. Q. Liu and I give a definition of viscosity solution of the principal eigenvalue problem for infinity Laplacian on metric spaces and show the existence of solution. S. Esaki, D. Kazukawa and I study Gromov's pyramids. In particular, we focus on sevenral fundamental functional inequality and show that their best constant become invariants of pyramids. Using them, we classify certain two infinite dimensional objects as pyramids.
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| Free Research Field |
アレクサンドロフ空間の収束・グロモフのピラミッド
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| Academic Significance and Societal Importance of the Research Achievements |
報告者が主に扱った研究対象は曲率の制限を持つ空間(アレクサンドロフ空間)およびある種の無限次元空間(グロモフの意味のピラミッド)である. また距離空間上の解析学について基礎研究も行った. また曲率の制限を持たない状況で多様体の自然な構成に関する連続性を論じた. これらはつまり, 様々な立場で距離空間や測度距離空間の収束理論を展開していると言える. 特に無限次元の空間の幾何の研究は世界的にまだ始まったばかりであり, 今後の発展が大いに期待できる.
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