Capacities on Levi-flat real hypersurfaces

• Project/Area Number: 18K13422
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: Shizuoka University
• Principal Investigator: Adachi Masanori 静岡大学, 理学部, 講師 (30708392)
• Project Period (FY): 2018-04-01 – 2024-03-31
• Project Status: Completed (Fiscal Year 2023)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2021: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: レビ平坦曲面 / 複素解析幾何 / 葉層構造論 / 多変数関数論 / 力学系理論 / CR幾何学 / 群作用 / 剛性理論 / 留数定理 / 円周への群作用 / 国際情報交換 / 剛性 / 正則接続 / 特性類の局所化 / ホッジ理論 / ポテンシャル論 / 対数接続 / 横断構造 / ソボレフ空間

Outline of Final Research Achievements

We investigated Levi-flat real hypersurfaces, important geometric objects in complex analysis in several variables and dynamical systems on holomorphic foliations. Our goal was to contribute to solving the generalized Levi problem and a conjecture by Cerveau. We focused on analyzing the typical examples of Levi-flats, particularly those found within flat ruled surfaces and Inoue-Hirzebruch surfaces. The highlight of our research was successfully confirming a conjecture by Brunella, achieved through collaboration with Judith Brinkschulte.

Academic Significance and Societal Importance of the Research Achievements

2次元複素射影空間に関するCerveau予想へのアプローチは道半ばとなったが、3次元以上のコンパクト複素多様体における余次元1正則葉層の極小集合の構造論に関して、Brunella予想の解決という2008年以来の大きな進展を得た。当初計画に沿う形でLevi平坦境界の領域の典型例における具体的な解析結果が複数得られた他、Diederich-Fornaess指数のCR幾何学的定式化、カスプ付き双曲曲面に関する松元型剛性定理の新証明など、当初計画で予期しなかった複数の成果も得られた。

Research Products

• [Int'l Joint Research] ライプチヒ大学(ドイツ)
• [Int'l Joint Research] オー=ド=フランス工科大学(フランス)
• [Int'l Joint Research] 基礎科学研究院(韓国)
• [Int'l Joint Research] ポリテクニック・オー=ド=フランス大学(フランス)
• [Int'l Joint Research] ライプチヒ大学(ドイツ)
• [Int'l Joint Research] ライプチヒ大学(ドイツ)
• [Int'l Joint Research] ポリテクニック・オー=ド=フランス大学(フランス)
• [Int'l Joint Research] 基礎科学研究所(韓国)
• [Int'l Joint Research] ポリテクニック・オー＝ド＝フランス大学(フランス)
• [Int'l Joint Research] ライプチヒ大学(ドイツ)
• [Int'l Joint Research] 釜山大学校(韓国)
• [Int'l Joint Research] ポリテクニック・オー＝ド＝フランス大学(フランス)
• [Int'l Joint Research] ライプチヒ大学(ドイツ)
• [Int'l Joint Research] ライプツィヒ大学(ドイツ)
• [Int'l Joint Research] アイスランド大学(アイスランド)
• [Journal Article] Dynamical aspects of foliations with ample normal bundle (2023)
  • Author(s): Masanori Adachi、Brinkschulte Judith
  • Journal Title: Indiana University Mathematics Journal Volume: 72 Issue: 5 Pages: 1931-1947
  • DOI: 10.1512/iumj.2023.72.9488
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A Residue Formula for Meromorphic Connections and Applications to Stable Sets of Foliations (2023)
  • Author(s): Adachi Masanori、Biard S?verine、Brinkschulte Judith
  • Journal Title: The Journal of Geometric Analysis Volume: 33 Issue: 10 Pages: 1-23
  • DOI: 10.1007/s12220-023-01385-9
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] On Levi flat hypersurfaces with transversely affine foliation (2022)
  • Author(s): Adachi Masanori、Biard Severine
  • Journal Title: Mathematische Zeitschrift Volume: 301 Issue: 1 Pages: 373-383
  • DOI: 10.1007/s00209-021-02927-z
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] On weighted Bergman spaces of a domain with Levi-flat boundary II (2022)
  • Author(s): Masanori Adachi
  • Journal Title: Complex Analysis and its Synergies Volume: 8 Issue: 2 Pages: 1-9
  • DOI: 10.1007/s40627-022-00097-0
  • Peer Reviewed
• [Journal Article] On weighted Bergman spaces of a domain with Levi-flat boundary (2021)
  • Author(s): M. Adachi
  • Journal Title: Trans. Amer. Math. Soc. Volume: 374 Issue: 10 Pages: 7499-7524
  • DOI: 10.1090/tran/8471
  • Peer Reviewed
• [Journal Article] Diederich-Fornaess and Steinness Indices for Abstract CR Manifolds (2021)
  • Author(s): Masanori Adachi, Jihun Yum
  • Journal Title: The Journal of Geometric Analysis Volume: － Issue: 8 Pages: 8385-8413
  • DOI: 10.1007/s12220-020-00598-6
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Weighted Bergman spaces of domains with Levi-flat boundary (2021)
  • Author(s): Masanori Adachi
  • Journal Title: 数理解析研究所講究録 Volume: 2175 Pages: 108-117
  • NAID: 40022530905
  • Open Access
• [Journal Article] Sobolev estimates for the complex Green operator on Levi-flat manifolds (2019)
  • Author(s): Masanori Adachi
  • Journal Title: 数理解析研究所講究録 Volume: 2137 Pages: 1-9
  • NAID: 40022147277
  • Open Access
• [Journal Article] On a hyperconvex manifold without non-constant bounded holomorphic functions (2018)
  • Author(s): Masanori Adachi
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 246 Pages: 1-10
  • DOI: 10.1007/978-981-13-1672-2_1
  • ISBN: 9789811316715, 9789811316722
  • Peer Reviewed
• [Presentation] 双曲井上曲面内のLevi平坦面について (2024)
  • Author(s): 足立真訓
  • Organizer: 第29回沼津改め静岡研究会 －幾何，複素解析，そして数理物理－
• [Presentation] Harmonic measures and rigidity for surface group actions on the circle (2024)
  • Author(s): 足立真訓
  • Organizer: 金沢トポロジーセミナー
  • Invited
• [Presentation] 有理型接続の留数定理と葉層の安定集合への応用 (2023)
  • Author(s): 足立真訓
  • Organizer: 2023年度多変数関数論冬セミナー
  • Invited
• [Presentation] On a Levi-flat hypersurface in hyperbolic Inoue surfaces (2023)
  • Author(s): M. Adachi
  • Organizer: 2023 Taipei Conference on Complex Geometry
  • Int'l Joint Research / Invited
• [Presentation] 有理型接続の留数定理と葉層の安定集合への応用 (2023)
  • Author(s): 足立真訓
  • Organizer: 葉層構造論シンポジウム
• [Presentation] A review on Levi-flat hypersurfaces and Bergman spaces (2023)
  • Author(s): M. Adachi
  • Organizer: Seminar in Oka Mathematical Institute
  • Invited
• [Presentation] 有理型接続の留数定理と葉層の安定集合への応用 (2023)
  • Author(s): 足立真訓,Severine Biard,Judith Brinkschulte
  • Organizer: 日本数学会2023年度秋季総合分科会函数論分科会
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2023)
  • Author(s): M. Adachi
  • Organizer: 29th Nordic Congress of Mathematicians
  • Int'l Joint Research / Invited
• [Presentation] Harmonic measures and rigidity for surface group actions on the circle (2023)
  • Author(s): 足立真訓
  • Organizer: 早稲田双曲幾何幾何学的群論セミナー
  • Invited
• [Presentation] On weighted Bergman spaces of a domain with Levi-flat boundary (2023)
  • Author(s): M. Adachi
  • Organizer: Oka Theory and Complex Geometry Conference, Summer 2023
  • Int'l Joint Research / Invited
• [Presentation] On weighted Bergman spaces of a domain with Levi-flat boundary (2023)
  • Author(s): M. Adachi
  • Organizer: SCV, CR geometry and Dynamics
  • Int'l Joint Research / Invited
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2023)
  • Author(s): 足立真訓
  • Organizer: 東京大学複素解析幾何セミナー
• [Presentation] A survey on Levi-flats and related topics (2023)
  • Author(s): 足立真訓
  • Organizer: 多変数函数論における擬凸性とその周辺
  • Invited
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2023)
  • Author(s): M. Adachi
  • Organizer: Seminaire "Analyse complexe et equations differentielles", Laboratoire Paul Painleve - CNRS
  • Int'l Joint Research / Invited
• [Presentation] The Levi problem and quantitative study in several complex variable (2023)
  • Author(s): M. Adachi
  • Organizer: Seminar at University of Milano-Bicocca
  • Int'l Joint Research / Invited
• [Presentation] Dynamical aspects of foliations with ample normal bundle (2022)
  • Author(s): M. Adachi
  • Organizer: Virtual East-West Several Complex Variables Seminar, (online)
  • Invited
• [Presentation] On weighted Bergman spaces of a domain with Levi-flat boundary (2022)
  • Author(s): M. Adachi
  • Organizer: CR Geometry and PDEs IX
  • Int'l Joint Research / Invited
• [Presentation] On weighted Bergman spaces of a domain with Levi-flat boundary (2022)
  • Author(s): M. Adachi
  • Organizer: Workshop on Complex Analysis and Geometry
  • Int'l Joint Research / Invited
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2022)
  • Author(s): M. Adachi
  • Organizer: HAYAMA Symposium on Complex Analysis in Several Variables XXIII
  • Int'l Joint Research / Invited
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2022)
  • Author(s): M. Adachi
  • Organizer: Complex Geometry Workshop
  • Int'l Joint Research / Invited
• [Presentation] On weighted Bergman spaces of a domain with Levi-flat boundary (2022)
  • Author(s): M. Adachi
  • Organizer: Journee Complexe, Laboratoire J.A. Dieudonne de l'Universite Cote d'Azur
  • Int'l Joint Research / Invited
• [Presentation] A residue formula for meromorphic connections and applications to stable sets of foliations (2022)
  • Author(s): M. Adachi
  • Organizer: Joint Seminar on Complex Algebraic Geometry and Complex Analysis
  • Int'l Joint Research / Invited
• [Presentation] Harmonic measures and rigidity for surface group actions on the circle (2022)
  • Author(s): M. Adachi
  • Organizer: 36th Summer Topology Conference
  • Int'l Joint Research / Invited
• [Presentation] Harmonic measures and rigidity for surface group actions on the circle (2022)
  • Author(s): 足立真訓
  • Organizer: 葉層構造論シンポジウム
• [Presentation] Dynamical aspects of foliations with ample normal bundle (2022)
  • Author(s): Masanori Adachi
  • Organizer: The Conference on Complex Geometric Analysis in honor of Kang-Tae Kim’s 65th birthday
  • Int'l Joint Research / Invited
• [Presentation] Dynamical aspects of foliations with ample normal bundle (2021)
  • Author(s): 足立真訓
  • Organizer: 葉層構造の幾何学とその応用
  • Invited
• [Presentation] 豊富な法束を持つ葉層の力学的様相 (2021)
  • Author(s): 足立真訓
  • Organizer: 2021年度多変数関数論冬セミナー
  • Invited
• [Presentation] Dynamical aspects of foliations with ample normal bundle (2021)
  • Author(s): 足立真訓
  • Organizer: 葉層構造論シンポジウム
• [Presentation] 豊富な法束を持つ葉層の力学的様相 (2021)
  • Author(s): 足立真訓, Judith Brinkschulte
  • Organizer: 2021年度日本数学会秋季総合分科会函数論分科会
• [Presentation] On Levi flat hypersurfaces with transversely affine foliation (2021)
  • Author(s): Masanori Adachi
  • Organizer: Grauert theory and recent complex geometry（大阪市立大学数学研究所）
  • Int'l Joint Research / Invited
• [Presentation] 横断的アフィン葉層を持つレビ平坦面について (2021)
  • Author(s): 足立真訓、Severine Biard
  • Organizer: 2021年度日本数学会年会函数論分科会
• [Presentation] On Levi flat hypersurfaces with transversely affine foliation (2020)
  • Author(s): Masanori Adachi
  • Organizer: Seminar semiklassische Analysis und Darstellungstheorie（ドイツ・ケルン大学）
  • Int'l Joint Research / Invited
• [Presentation] On Levi flat hypersurfaces with transversely affine foliation (2020)
  • Author(s): Masanori Adachi
  • Organizer: 東京大学複素解析幾何セミナー
• [Presentation] Diederich-Fornaess and Steinness indices for abstract CR manifolds (2020)
  • Author(s): 足立真訓
  • Organizer: 東京大学複素解析幾何セミナー
• [Presentation] 複素多様体内の弱擬凸領域に対するDiederich-Fornaess指数とStein性指数 (2020)
  • Author(s): 足立真訓, Jihun Yum
  • Organizer: 2020年度日本数学会年会函数論分科会
• [Presentation] Ampleness of positive CR line bundles over Levi-flat manifolds, revisited (2019)
  • Author(s): Masanori Adachi
  • Organizer: The POSTECH Conference 2019 on Complex Analytic Geometry: The KSCV13
  • Int'l Joint Research / Invited
• [Presentation] The Diederich-Fornaess index and Steinness index (2019)
  • Author(s): Masanori Adachi
  • Organizer: IMS Pacific Rim Complex-Symplectic Geometry Conference in 2019
  • Int'l Joint Research / Invited
• [Presentation] レビ平坦多様体上のソボレフ評価について (2019)
  • Author(s): 足立真訓
  • Organizer: 東京理科大学理工学部数学科談話会
  • Invited
• [Presentation] The Diederich-Fornaess index and Steinness index (2019)
  • Author(s): Masanori Adachi
  • Organizer: International Conference on Complex Analysis dedicated to the memory of Andrei Gonchar and Anatoliy Vitushkin
  • Int'l Joint Research / Invited
• [Presentation] Sobolev estimates for the complex Green operator on Levi-flat manifolds II (2019)
  • Author(s): Masanori Adachi
  • Organizer: RIMS共同研究(グループ型) Geometric Complex Analysis on Foliations and Dynamics
  • Invited
• [Presentation] Ergodic and Liouville property for domains with Levi-flat boundary (2019)
  • Author(s): Masanori Adachi
  • Organizer: 2019 PNU Math Forum
  • Int'l Joint Research / Invited
• [Presentation] On a hyperconvex manifold without non-constant bounded holomorphic functions (2019)
  • Author(s): Masanori Adachi
  • Organizer: 2019 Taipei conference on complex geometry
  • Int'l Joint Research / Invited
• [Presentation] On the normal bundle of Levi-flat real hypersurfaces (2019)
  • Author(s): Masanori Adachi
  • Organizer: Workshop on Complex Analytic and Algebraic Methods in Dynamics
  • Int'l Joint Research / Invited
• [Presentation] レビ平坦多様体の小平型埋め込みについて (2019)
  • Author(s): 足立真訓
  • Organizer: 東京理科大学理工学部数学科談話会
  • Invited
• [Presentation] 双曲閉曲面の測地流のエルゴード性と超幾何関数 (2019)
  • Author(s): 足立真訓
  • Organizer: 第26回 沼津改め静岡研究会 －幾何，数理物理，そして量子論－
  • Invited
• [Presentation] On a hyperconvex manifold without non-constant bounded holomorphic functions (2019)
  • Author(s): Masanori Adachi
  • Organizer: Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry
  • Int'l Joint Research
• [Presentation] Weighted Bergman spaces of domains with Levi-flat boundary (2018)
  • Author(s): Masanori Adachi
  • Organizer: KIAS Workshop: Progress in Several Complex Variables
  • Int'l Joint Research / Invited
• [Presentation] 閉リーマン面上の相補的な正則円板束 (2018)
  • Author(s): 足立真訓
  • Organizer: 名城大学ポテンシャル論セミナー
  • Invited
• [Presentation] On a hyperconvex manifold without non-constant bounded holomorphic functions (2018)
  • Author(s): Masanori Adachi
  • Organizer: Complex geometry and complex dynamics in higher dimensions
  • Int'l Joint Research / Invited
• [Presentation] 非定数有界正則関数を持たない超凸多様体 (2018)
  • Author(s): 足立真訓
  • Organizer: 2018年度日本数学会秋季総合分科会函数論分科会
• [Presentation] レビ平坦面上の中野型消滅定理たち (2018)
  • Author(s): 足立真訓
  • Organizer: 名古屋大学解析幾何学セミナー
• [Presentation] On certain hyperconvex manifolds without non-constant bounded holomorphic functions (2018)
  • Author(s): 足立真訓
  • Organizer: 東京大学複素解析幾何セミナー
• [Presentation] フックス群の対角作用で不変な二重円板上の正則関数について (2018)
  • Author(s): 足立真訓
  • Organizer: 早稲田整数論セミナー
  • Invited
• [Presentation] Ampleness of positive CR line bundles over Levi-flat manifolds, revisited (2018)
  • Author(s): Masanori Adachi
  • Organizer: ESI Workshop: Analysis and CR geometry
  • Int'l Joint Research / Invited
• [Presentation] Sobolev estimates for the complex Green operator on Levi-flat manifolds (2018)
  • Author(s): Masanori Adachi
  • Organizer: RIMS Workshop: Symmetry and Singularity of Geometric Structures and Differential Equations
  • Int'l Joint Research / Invited
• [Remarks] 研究代表者のWebページ
  • URL: https://wwp.shizuoka.ac.jp/masanori-adachi/
• [Remarks] プレプリント（Biard氏、Brinkschulte氏との共著論文、投稿中）
  • URL: https://arxiv.org/abs/2210.09273
• [Remarks] プレプリント（松田氏、野澤氏との共著論文、投稿中）
  • URL: https://arxiv.org/abs/2207.08411
• [Remarks] 報告者の執筆した論文・予稿など
  • URL: https://wwp.shizuoka.ac.jp/masanori-adachi/
• [Remarks] プレプリント(J. Brinkschulte氏との共著、Indiana UMJに掲載決定)
  • URL: https://arxiv.org/abs/2105.10226
• [Remarks] プレプリント(Severine Biard 氏との共著論文、投稿中)
  • URL: http://arxiv.org/abs/2011.06379
• [Remarks] プレプリント（釜山大学校 Jihun Yum 氏との共著論文、投稿中）
  • URL: https://arxiv.org/abs/2003.01330
• [Funded Workshop] Young Mathematicians Workshop on Several Complex Variables 2019 (2019)
• [Funded Workshop] Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry (2019)