Geometric Analysis on non-compact spaces and the geometry of infinite dimensional moduli spaces

• Project/Area Number: 21740048
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: TSUKAMOTO Masaki 京都大学, 大学院・理学研究科, 助教 (70527879)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: 微分幾何 / 複素解析 / 力学系 / 無限次元 / 非コンパクト空間 / モジュライ空間 / 平均次元 / 非コンパクト / モジュライ

Research Abstract

I concentrate on the most important results. I constructed an example of oriented complete Riemannian 4-manifolds having no non-trivial instanton. We studied moduli spaces of ASD connections whose curvatures are uniformly bounded over the product space of 3-sphere and the line. We got an estimate relating their local mean dimension to the energy densities of connections. We got an estimate relating a mean dimension of the space of Brody curves to the energy densities of curves. In particular we got an exact formula which represents the mean dimension by using the energy densities in the case that the target space is the Riemann sphere.

Research Products

• [Journal Article] Remark on dynamical Morse inequality, Proceedings of the Japan Academy, Series A (2011)
  • Author(s): Masayuki Asaoka, Tomohiro Fukaya, Masaki Tsukamoto
  • Journal Title: Mathematical Sciences Volume: Vol.87 Pages: 178-182
  • Peer Reviewed
• [Journal Article] An open 4-manifoldhaving no instant (2011)
  • Author(s): Masaki Tsukamoto
  • Journal Title: Annals of Global Analysis and Geometry Volume: vol.40 Issue: 3 Pages: 251-286
  • DOI: 10.1007/s10455-011-9256-2
  • Peer Reviewed
• [Journal Article] Instant on approximation, periodic AS Dconnections, and mean dimension (2011)
  • Author(s): Shinichiroh Matsuo, Masaki Tsukamoto
  • Journal Title: Journal of Functional Analysis Volume: Vol.260 Issue: 5 Pages: 1369-1427
  • DOI: 10.1016/j.jfa.2010.11.008
  • Peer Reviewed
• [Journal Article] Remark on dynamical Morse inequality (2011)
  • Author(s): Masayuki Asaoka, Tomohiro Fukaya, Masaki Tsukamoto
  • Journal Title: Proceedings of the Japan Academy, Series A, Mathematical Sciences Volume: 87 Issue: 9 Pages: 178-182
  • DOI: 10.3792/pjaa.87.178
  • NAID: 40019128083
  • Peer Reviewed
• [Journal Article] Instanton approximation, periodic ASD connections, and mean dimension (2010)
  • Author(s): Shinichiroh Matsuo, Masaki Tsukamoto
  • Journal Title: Journal of Functional Analysis Volume: 260 Pages: 1369-1427
  • Peer Reviewed
• [Journal Article] A packing problem for holomorphic curves (2009)
  • Author(s): Masaki Tsukamoto
  • Journal Title: Nagoya Mathematical Journal 194 Pages: 33-68
  • Peer Reviewed
• [Journal Article] Deformation of Brody curves and mean dimension (2009)
  • Author(s): Masaki Tsukamoto
  • Journal Title: Ergodic Theory and Dynamical Systems 29 Pages: 1641-1657
  • Peer Reviewed
• [Journal Article] Gauge theory on infinite connected sum and mean dimension (2009)
  • Author(s): Masaki Tsukamoto
  • Journal Title: Mathematical Physics, Analysis and Geometry 12 Pages: 325-380
  • Peer Reviewed
• [Journal Article] Asymptotic distribution of critical values (2009)
  • Author(s): Tomohiro Fukaya
  • Journal Title: Geometriae Dedicata 143 Pages: 63-67
  • Peer Reviewed
• [Journal Article] An open 4-manifold having no instanton
  • Author(s): Masaki Tsukamoto
  • Journal Title: Annals of Global Analysis and Geometry Volume: (To appear)
  • Peer Reviewed
• [Presentation] Brody curves and mean dimension (2012)
  • Author(s): Masaki Tsukamoto
  • Organizer: Joint Geometric Analysis/Function Theory Seminar
  • Place of Presentation: Purdue University(米国)
  • Year and Date: 2012-03-21
• [Presentation] Brody curves and mean dimension (2012)
  • Author(s): Masaki Tsukamoto
  • Organizer: Joint Geometric Analysis/ Function Theory Seminar
  • Place of Presentation: Purdue University(米国)(招待講演)
  • Year and Date: 2012-03-21
• [Presentation] ブロディ曲線と平均次元 (2012)
  • Author(s): 塚本真輝
  • Organizer: 東工大複素解析セミナー
  • Place of Presentation: 東京工業大学(招待講演)
  • Year and Date: 2012-01-17
• [Presentation] Brody curves and mean dimension (2012)
  • Author(s): Masaki Tsukamoto
  • Organizer: 第7回日中友好幾何学研究集会
  • Place of Presentation: ホテルレジーナ河口湖(山梨県)
  • Year and Date: 2012-01-13
• [Presentation] Brody curves and mean dimension (2012)
  • Author(s): Masaki Tsukamoto
  • Organizer: 第7回日中友好幾何学研究集会
  • Place of Presentation: ホテルレジーナ河口湖(山梨県)(招待講演)
  • Year and Date: 2012-01-13
• [Presentation] Brody curves and mean dimension (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: Group Actions Seminar
  • Place of Presentation: Hebrew University(イスラエル)
  • Year and Date: 2011-12-01
• [Presentation] Brody curves and mean dimension (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: Group Actions Seminar
  • Place of Presentation: Hebrew University(イスラエル)(招待講演)
  • Year and Date: 2011-12-01
• [Presentation] 非コンパクト4次元多様体上のゲージ理論 (2011)
  • Author(s): 塚本真輝
  • Organizer: 日本数学会特別講演
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-28
• [Presentation] 非コンパクト4次元多様体上のゲージ理論 (2011)
  • Author(s): 塚本真輝
  • Organizer: 日本数学会特別講演
  • Place of Presentation: 信州大学(招待講演)
  • Year and Date: 2011-09-28
• [Presentation] An open 4-manifoldhaving no instant (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: 2011 Complex Geometry and Symplectic Geometry Conference
  • Place of Presentation: University of Science and Technology of China(中国)
  • Year and Date: 2011-08-15
• [Presentation] An open 4-manifold having no instanton (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: 2011 Complex Geometry and Symplectic Geometry Conference
  • Place of Presentation: University of Science and Technology of China(中国)(招待講演)
  • Year and Date: 2011-08-15
• [Presentation] 平均次元と埋め込み問題 (2011)
  • Author(s): 塚本真輝
  • Organizer: 京都力学系セミナー
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2011-07-01
• [Presentation] 開4次元多様体上のゲージ理論 (2011)
  • Author(s): 塚本真輝
  • Organizer: 幾何学セミナー
  • Place of Presentation: 九州大学(招待講演)
  • Year and Date: 2011-05-13
• [Presentation] 開4次元多様体上のゲージ理論 (2011)
  • Author(s): 塚本真輝
  • Organizer: 臨時講演会
  • Place of Presentation: 京都大学(日本数学会年会中止に伴う 招待講演)
  • Year and Date: 2011-03-22
• [Presentation] Deformation of Brody curves and mean dimension (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: Dynamics and Probability Seminar
  • Place of Presentation: Hebrew University(イスラエル)
  • Year and Date: 2011-03-15
• [Presentation] Deformation of Brody curves and mean dimension (2011)
  • Author(s): Masaki Tsukamoto
  • Organizer: Dynamics and Probability Seminar
  • Place of Presentation: Hebrew University (Israel)(招待講演)
  • Year and Date: 2011-03-15
• [Presentation] 平均次元入門 (2011)
  • Author(s): 塚本真輝
  • Organizer: フラクタルの数学的諸相
  • Place of Presentation: かんぽの宿 山代(石川県)(招待講演)
  • Year and Date: 2011-02-22
• [Presentation] On Bertelson-Gromov's dynamical Morse inequality (2010)
  • Author(s): Masaki Tsukamoto
  • Organizer: Doctorial Forum of Mathematics between Fudan and Kyoto Universities
  • Place of Presentation: Fudan University (China)(招待講演)
  • Year and Date: 2010-11-04
• [Presentation] インスタントンを持たない開4次元多様体 (2010)
  • Author(s): 塚本真輝
  • Organizer: 日本数学会 秋季総合分科会 幾何学分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] インスタントンを持たない開4次元多様体 (2010)
  • Author(s): 塚本真輝
  • Organizer: 幾何学シンポジウム
  • Place of Presentation: 神戸大学(招待講演)
  • Year and Date: 2010-08-08
• [Presentation] インスタントンを持たない開4次元多様体 (2010)
  • Author(s): 塚本真輝
  • Organizer: 微分トポロジーセミナー
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2010-06-22
• [Presentation] 力学モース理論についての考察 (2010)
  • Author(s): 塚本真輝
  • Organizer: 幾何学コロキウム
  • Place of Presentation: 北海道大学(招待講演)
  • Year and Date: 2010-06-08
• [Presentation] インスタントンを持たない開4次元多様体 (2010)
  • Author(s): 塚本真輝
  • Organizer: NLPDEセミナー
  • Place of Presentation: 京都大学(招待講演)
  • Year and Date: 2010-05-21
• [Presentation] An introduction to Gromov's mean dimension theory (2010)
  • Author(s): 塚本真輝
  • Organizer: First friendship meeting in mathematics between Fudan and Kyoto Universities
  • Place of Presentation: 京都大学
  • Year and Date: 2010-01-15
• [Presentation] 無限連結和上のゲージ理論と平均次元 (2009)
  • Author(s): 塚本真揮
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] Instant on approximation, periodic ASD connections, and meandimension (2009)
  • Author(s): 塚本真輝
  • Organizer: The XX1st Rolf Nevanlinna Colloquium
  • Place of Presentation: 京都大学
  • Year and Date: 2009-09-07
• [Presentation] Instanton approximation, periodic ASD connections, and mean dimension (2009)
  • Author(s): 塚本真輝
  • Organizer: The XXIst Rolf Nevanlinna Colloquium
  • Place of Presentation: 京都大学
  • Year and Date: 2009-09-07
• [Presentation] インスタントン近似,周期ASD接続,そして平均次元 (2009)
  • Author(s): 塚本真輝
  • Organizer: 代数幾何の関連する諸分野
  • Place of Presentation: 北海道大学
  • Year and Date: 2009-09-03
• [Presentation] インスタントン近似,周期ASD接続,そして平均次元 (2009)
  • Author(s): 塚本真輝
  • Organizer: 東京幾何セミナー
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-07-24
• [Presentation] The geometry of the space of Brody curves and mean dimension (2009)
  • Author(s): 塚本真輝
  • Organizer: 第13回多変数関数論葉山シンポジウム
  • Place of Presentation: 湘南国際村センター(神奈川県)
  • Year and Date: 2009-07-22
• [Presentation] The geometry of the space of Brody curves and mean dimension (2009)
  • Author(s): 塚本真輝
  • Organizer: 第13回多変数関数論葉山シンポジウム
  • Place of Presentation: 湘南国際村センター
  • Year and Date: 2009-07-22
• [Presentation] The geometry of themoduli space of Brody curves (2009)
  • Author(s): Masaki Tsukamoto
  • Organizer: 1^<st> PRIM Congress
  • Place of Presentation: University of New South Wales(オーストラリア)
  • Year and Date: 2009-07-07
• [Presentation] The geometry of the moduli space of Brody curves (2009)
  • Author(s): Masaki Tsukamoto
  • Organizer: 1^<st> PRIMA Congress
  • Place of Presentation: University of New South Wales(英国)
  • Year and Date: 2009-07-07
• [Presentation] Asymptotic distribution of critical values (2009)
  • Author(s): 塚本真輝
  • Organizer: Friday Seminar on Knot Theory
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2009-05-29
• [Presentation] Brody曲線の空間の幾何と平均次元 (2009)
  • Author(s): 塚本真輝
  • Organizer: 複素解析幾何セミナー
  • Place of Presentation: 東京大学
  • Year and Date: 2009-05-25
• [Presentation] A survey of mean dimension (2009)
  • Author(s): 塚本真輝
  • Organizer: 微分トポロジーセミナー
  • Place of Presentation: 京都大学
  • Year and Date: 2009-04-14