Updated on 2021/10/21

写真a

 
FUJINO Hiroki
 
Organization
Institute for Advanced Research Designated assistant professor
Graduate School of Mathematics Designated assistant professor
Title
Designated assistant professor

Degree 1

  1. Ph. D. (Mathematical science) ( 2017.3   Nagoya University ) 

Research Interests 5

  1. maximal surface

  2. minimal surface

  3. harmonic function theory

  4. Teichmuller theory

  5. quasiconformal mapping

Research Areas 2

  1. Natural Science / Basic analysis

  2. Natural Science / Geometry

Current Research Project and SDGs 2

  1. 反ド・ジッター空間における曲面論と普遍タイヒミュラー理論との相互的研究

  2. Degenerations in infinite dimensional Teichmuller spaces

Education 2

  1. Nagoya University   Graduate School, Division of Mathematical Sciences

    - 2017.3

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    Country: Japan

  2. Nagoya University   Faculty of Science

    2008.4 - 2012.3

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    Country: Japan

Professional Memberships 1

  1. 日本数学会

Awards 2

  1. 名古屋大学学術奨励賞

    2016.7   名古屋大学  

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    Country:Japan

  2. 平成 25 年度多元数理修士論文賞

    2014.3   多元数理科学研究科   C-Zとの擬等角同値性について

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    Country:Japan

    リンク情報:http://www.cajpn.org/refs/thesis.html

 

Papers 6

  1. Reflection principle for lightlike line segments on maximal surfaces Reviewed

    Shintaro Akamine, Hiroki Fujino

    Ann. Global Anal. Geom.     2020

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    Language:English   Publishing type:Research paper (scientific journal)  

    As in the case of minimal surfaces in the Euclidean 3-space, the reflection principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if a maximal surface has a spacelike line segment L, the surface is invariant under the 180 degree-rotation with respect to L. However, such a reflection property does not hold for lightlike line segments on the boundaries of maximal surfaces in general.
    In this paper, we show some kind of reflection principle for lightlike line segments on the boundaries of maximal surfaces when lightlike line segments are connecting shrinking singularities. As an application, we construct various examples of periodic maximal surfaces with lightlike lines from tessellations of the plane.

    DOI: 10.1007/s10455-020-09743-4

  2. Extension of Krust theorem and deformations of minimal surfaces

    Hiroki Fujino;Shintaro Akamine

    arXiv:2110.0074     2021.10

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    In the minimal surface theory, the Krust theorem asserts that if a minimal surface in the
    Euclidean 3-space $\mathbb{E}^3$ is the graph of a function over a convex domain,
    then each surface of its associated family is also a graph. The same is true for maximal
    surfaces in the Minkowski 3-space $\mathbb{L}^3$.
    In this article, we introduce a new deformation family that continuously connects
    minimal surfaces in $\mathbb{E}^3$ and maximal surfaces in $\mathbb{L}^3$, and
    prove a Krust-type theorem for this deformation family. This result induces Krust-type
    theorems for various important deformation families containing the associated family
    and the L\'opez-Ros deformation.
    Furthermore, minimal surfaces in the isotropic 3-space $\mathbb{I}^3$ appear in the
    middle of the above deformation family. We also prove another type of Krust's theorem
    for this family, which implies that the graphness of such minimal surfaces in
    $\mathbb{I}^3$ strongly affects the graphness of deformed surfaces.
    The results are proved based on the recent progress of planar harmonic mapping
    theory.

  3. Duality of boundary value problems for minimal and maximal surfaces

    Shintaro Akamine, Hiroki Fujino

        page: 1-26    2019.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    In 1966, Jenkins and Serrin gave existence and uniqueness results for infinite boundary value problems of minimal surfaces in the Euclidean space, and after that such solutions have been studied by using the univalent harmonic mapping theory. In this paper, we show that there exists a one-to-one correspondence between solutions of infinite boundary value problems for minimal surfaces and those of lightlike line boundary problems for maximal surfaces in the Lorentz-Minkowski spacetime.
    We also investigate some symmetry relations associated with the above correspondence together with their conjugations, and observe function theoretical aspects of the geometry of these surfaces. Finally, a reflection property along lightlike line segments on boundaries of maximal surfaces is discussed.

  4. Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra, and 5D AGT correspondence

    Awata Hidetoshi, Fujino Hiroki, Ohkubo Yusuke

    JOURNAL OF MATHEMATICAL PHYSICS   Vol. 58 ( 7 )   2017.7

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1063/1.4993773

    Web of Science

    Scopus

  5. QUASISYMMETRIC EMBEDDING OF THE INTEGER SET AND ITS QUASICONFORMAL EXTENSION

    Fujino Hiroki

    ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA   Vol. 42 ( 2 ) page: 575-584   2017

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.5186/aasfm.2017.4230

    Web of Science

    Scopus

  6. The existence of quasiconformal homeomorphism between planes with countable marked points Reviewed

    Hiroki Fujino

    Kodai Mathematical Journal   Vol. 38 ( 3 ) page: 732-764   2015

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2996/kmj/1446210604

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MISC 2

  1. 極小ラグランジュ擬等角写像のベルトラミ係数について

    藤野弘基

    北海道大学数学講究録(第14回数学総合若手研究集会テクニカルレポート)   Vol. 173   page: 339-348   2018.2

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    Authorship:Lead author   Language:Japanese  

  2. 極小ラグランジュ擬等角写像のベルトラミ係数について

    藤野弘基

    第60回関数論シンポジウム講演アブストラクト(日本数学会, 関数論分科会)     page: 27-44   2017.10

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    Authorship:Lead author   Language:Japanese  

Presentations 43

  1. Extension of Krust Theorem and Deformations of Minimal Surfaces

    多元数理科学研究科セミナー  2021.10.12 

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    Event date: 2021.10

  2. 調和関数の不連続境界値における鏡像の原理と曲面論への応用

    藤野弘基

    大阪市立大複素解析セミナー  2021.5.13 

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    Event date: 2021.5

    Venue:オンライン  

  3. Reflection principle for lightlike line segments on maximal surfaces

    Hiroki Fujino, Shintaro Akamine

    2021.3.15 

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    Event date: 2021.3

    Presentation type:Oral presentation (general)  

  4. 極大曲面の境界上に現れる光的線分に対する関数論からの考察

    藤野弘基

    研究集会「多様体上の微分方程式」第22回  2020.11.26 

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    Event date: 2020.11

    Presentation type:Oral presentation (general)  

    Venue:オンライン開催  

  5. How to make complicated surfaces?

    Hiroki Fujino

    The 22nd YLC seminar  2020.10.27 

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    Event date: 2020.10

    Presentation type:Oral presentation (general)  

    Venue:Nagoya university  

  6. 極大曲面に対する光的線分境界値問題の可解性について

    藤野弘基

    大阪大学トポロジーセミナー  2020.10.7 

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    Event date: 2020.10

    Presentation type:Oral presentation (general)  

    Venue:大阪市立大学(現地とオンラインの同時開催)  

  7. 極小曲面論におけるベルンシュタインの問題と単葉調和関数論

    藤野弘基

    第2回 複素解析学オンライン研究交流会   2020.10.2 

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    Event date: 2020.10

    Presentation type:Oral presentation (general)  

    Venue:オンライン開催  

  8. 単葉調和関数および極小曲面・極大曲面に対する境界値問題の対応

    藤野 弘基, 赤嶺 新太郎

    2020年度秋季日本数学会   2020.9.22 

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    Event date: 2020.9

    Presentation type:Oral presentation (general)  

  9. Reflection principles for minimal or maximal surfaces International conference

    Hiroki Fujino

    Workshop on Geometric Function Theory and Special Functions III 

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    Event date: 2020.2

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  10. 単葉調和関数論から見た極小・極大曲面論 International conference

    藤野弘基

    東工大複素解析セミナー 

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    Event date: 2020.1

    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:東京工業大学大岡山キャンパス   Country:Japan  

  11. L3 内の極大曲面の拡張性と対称性, および周期曲面 International conference

    藤野弘基

    2019 年度「リーマン面・不連続群論」研究集会 

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    Event date: 2020.1

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  12. 単葉調和関数論から見た極小・極大曲面論

    藤野弘基

    大阪市立大学複素解析セミナー 

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    Event date: 2019.12

    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Venue:大阪市立大学   Country:Japan  

  13. Duality of boundary value problems of minimal and maximal surfaces International conference

    Hiroki Fujino

    The 3rd International Workshop Geometry of Submanifolds and Integrable Systems 

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    Event date: 2019.12

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  14. 単葉調和函数論から見た極小・極大曲面論

    藤野弘基

    関数論若手勉強会 at 金沢 

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    Event date: 2019.11

    Language:Japanese   Presentation type:Public lecture, seminar, tutorial, course, or other speech  

    Country:Japan  

  15. 極小・極大グラフ間の双対性に対する単葉調和関数論からの考察 Invited

    藤野弘基

    早稲田双曲幾何幾何学的群論セミナー 

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    Event date: 2019.5

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:早稲田大学   Country:Japan  

  16. 反ド・ジッター空間における極大曲面論と普遍タイヒミュラー理論 Invited

    藤野弘基

    Beltrami 方程式勉強会 PartII 

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    Event date: 2019.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:東京工業大学   Country:Japan  

  17. 反ド・ジッター空間内の完備極大曲面に対する表現公式 Invited

    藤野弘基

    静岡複素解析幾何セミナー 

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    Event date: 2019.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:静岡大学   Country:Japan  

  18. Representation formula for complete maximal surfaces in AdS3 Invited International conference

    Hiroki Fujino

    Geometric Function Theory and Related Topics 

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    Event date: 2019.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Tohoku university   Country:Japan  

  19. 反ド・ジッター空間内の曲面論と普遍タイヒミュラー理論 Invited

    藤野弘基

    等角写像・値分布論合同研究集会 

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    Event date: 2018.12

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:大阪府立大学   Country:Japan  

  20. 極小ラグランジュ擬等角写像のベルトラミ係数について Invited

    藤野弘基

    複素領域における関数方程式とその周辺 

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    Event date: 2018.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:広島大学   Country:Japan  

  21. 極小ラグランジュ擬等角写像のベルトラミ係数について

    藤野弘基

    第 14 回 数学総合若手研究集会 

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    Event date: 2018.2 - 2018.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:北海道大学   Country:Japan  

  22. 極小ラグランジュ擬等角写像のベルトラミ係数について Invited

    藤野弘基

    函数論シンポジウム 

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    Event date: 2017.10

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:セントコア山口 (山口県)   Country:Japan  

  23. Ahlfors-Bers によるBeltrami 方程式の解法について Invited

    藤野弘基

    Beltrami 方程式勉強会 PartI 

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    Event date: 2017.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:東京工業大学   Country:Japan  

  24. Minimal Lagrangian 擬等角写像のBeltrami 係数について

    藤野弘基

    第 52 回函数論サマーセミナー (2017 年度) 

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    Event date: 2017.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:かんぽの宿柳川(福岡県)   Country:Japan  

  25. Extension theory for quasisymmetric embeddings of planar subsets Invited

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    Event date: 2017.1

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  26. Quasisymmetric embedding of discrete subset and its extendability Invited International conference

    Hiroki Fujino

    Young Mathematicians Workshop on Several Complex Variables 2016 

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    Event date: 2016.11

    Language:English   Presentation type:Oral presentation (general)  

    Venue:University of Tokyo   Country:Japan  

  27. Bonsante–Schlenker 「Maximal surfaces and the universal Teichmuller space」の解説 Invited

    藤野弘基

    双曲幾何と AdS 空間 

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    Event date: 2016.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:名古屋大学   Country:Japan  

  28. Quasisymmetric embedding of the integer set and its quasiconformal extension

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    Event date: 2016.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  29. 整数点集合の擬対称埋め込みの拡張性について

    藤野弘基

    第 51 回函数論サ マーセミナー (2016 年度) 

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    Event date: 2016.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:ホテル石風(山梨県)   Country:Japan  

  30. Quasisymmetric embeddings of the integer set and its quasiconformal extensions Invited International conference

    Hiroki Fujino

    Workshop on Geometric Function Theory and Special Functions 

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    Event date: 2016.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Tohoku university   Country:Japan  

  31. BeurlingAhlfors 拡張の Beltrami 係数の可積分性について

    藤野弘基

    第 50 回函数論サマーセミナー (2015 年度) 

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:あだたらふれあいセンター (福島県)   Country:Japan  

  32. DingIohara 代数のレベル 2 表現の結晶化

    粟田英資, 藤野弘基, 大久保勇輔

    2015 年度秋季日本数学会 

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:京都産業大学   Country:Japan  

  33. On the classification of planes with countable marked points up to quasiconformal equivalence International conference

    Hiroki Fujino

    The 23rd International Conference on Finite or Infinite Dimensional Complex Analysis and Applications (23rd ICFIDCAA) 

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    Event date: 2015.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Kyushu Sangyo University   Country:Japan  

  34. The existence of quasiconformal homeomorphism between planes with countable marked points International conference

    Hiroki Fujino

    Young Mathematicians Workshop on Several Complex Variables 2015 

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    Event date: 2015.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Tongji University, Shanghai, P. R. China   Country:China  

  35. On the classification of planes with countable marked points up to quasiconformal equivalence International conference

    Hiroki Fujino

    the 10th International Society for Analysis, its Applications and Computation (ISAAC 2015) 

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    Event date: 2015.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:the University of Macau, Macao, China SAR   Country:Macao  

  36. The existence of quasiconformal homeomorphism between planes with countable marked points Invited

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    Event date: 2015.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Country:Japan  

  37. 調和関数の不連続境界値における鏡像の原理と曲面論への応用

    藤野弘基

    大阪市立大複素解析セミナー  2021.5.13 

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    Venue:オンライン  

  38. 極大曲面の境界上に現れる光的線分に対する 関数論からの考察

    藤野 弘基

    研究集会「多様体上の微分方程式」第22回  2020.11.26 

  39. How to Make Complicated Surfaces?

    Hiroki Fujino

    22nd YLC seminar  2020.10.27 

  40. 極大曲面に対する光的線分境界値問題の可解性について

    藤野 弘基

    大阪大学トポロジーセミナー  2020.10.7 

  41. 極小曲面論におけるベルンシュタインの問題と単葉調和関数論

    藤野 弘基

    第2回 複素解析学オンライン研究交流会  2020.10.2 

  42. 単葉調和関数および極小曲面・極大曲面に対する 境界値問題の対応

    藤野 弘基, 赤嶺 新太郎

    2020年度秋季日本数学会  2020.9.22 

  43. 擬対称埋め込みの擬等角拡張性に関する近年の進展について

    藤野弘基

    山口大学複素解析セミナー, 山口大学  2017.2 

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KAKENHI (Grants-in-Aid for Scientific Research) 2

  1. 反ド・ジッター空間における曲面論と普遍タイヒミュラー理論との相互的研究

    2020.4 - 2023.3

    科学研究費補助金 

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    Authorship:Principal investigator 

    本研究の目的は、反ド・ジッター空間内の極大曲面の成す空間と普遍タイヒミュラー空間との間の一対一対応(Bonsante-Schlenker、2010)を 用いて双方の空間を調べることである。例えば与えられた極大曲面に対しその等長類がどの程度存在するか、対応するリーマン面の変形族を調 べ明らかにする。これは曲面論における重要な問題をタイヒミュラー理論の応用として解決するものである。逆に、無限次元タイヒミュラー空 間特有の退化現象について曲面論を用いた解析を行うことも目指す。
    本研究は、タイヒミュラー理論と曲面論、それぞれの分野で培われてきた強力な研究手法を他方の研究分野に相互的に応用しあうものである。

  2. 無限次元タイヒミュラー空間における退化現象の研究

    2018.10 - 2020.3

    科学研究費補助金  研究活動スタート支援

    藤野弘基

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    Authorship:Principal investigator 

 

Teaching Experience (On-campus) 2

  1. 数学演習I

    2020

  2. 数学演習V,VI

    2018