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Researcher Information

last modified：2024/01/08

Professor　Hideki Miyachi

Laboratory Website

Faculty, Affiliation

Faculty of Mathematics and Physics, Institute of Science and Engineering

College and School Educational Field

Division of Mathematical and Physical Science, Graduate School of Natural Science and Technology
Division of Mathematical and Physical Sciences, Graduate School of Natural Science and Technology
Course in Mathematics, School of Mathematics and Physics, College of Science and Engineering

Laboratory

　TEL:076-264-5647　FAX:076-264-5738

Academic Background

Career

Japan society for the promotion of science　Osaka city university　Research fellowship for young scientists(2000/04/01-2003/03/31)
Osaka University(2003/04/01-2003/09/30)
Osaka University(2003/10/01-2004/03/31)
Tokyo Denki University　Associate professor(2004/04/01-2007/03/31)
Tokyo Denki University　Associate professor(2007/04/01-2007/09/30)
Osaka university　Associate professor(2007/10/01-2018/03/31)
Kanazawa university　Professor(2018/04/01-)

Year & Month of Birth

Academic Society

Award

○MSJ Analysis Prize(2020/09)
○MSJ Analysis Prize(2020/09)

Specialities

Basic analysis

Speciality Keywords

Complex analysis, Teichmuller space, Moduli space, Riemann surface, Quasiconformal mapping, Hyperbolic geometry, Discrete group

Research Themes

Books

Papers

  • 　Pluripotential theory on Teichmüller space I: Pluricomplex Green function　Hideki Miyachi　Conformal Geometry and Dynamics　23　221--250　2019　
  • 　Geometry of the Gromov product: Geometry at infinity of Teichmueller space 　Hideki Miyachi　Journal of Mathematical Society of Japan　69　995-1049　2017
  • 　Convergence of Teichmüller deformations in the universal Teichmüller space　Hideki Miyachi, Dragomir Saric　Proceedings of the American Mathematical Society　147　11　4877-4889　2019
  • 　A dynamical approach to the infinitesimal spaces of quasiconformal mappings　Hideki Miyachi　Proceedings of American Mathematical Society　147　215-227　2019　
  • 　Extremal length functions are log-plurisubharmonic 　Hideki Miyachi　Tradition of Ahlfors–Bers, VII, Contemporary mathematics　696　225-250　2017

show all

  • 　Null-set compactifications of Teichmuller spaces 　Vincent Alberge, Hideki Miyachi and Ken'ichi Ohshika (in alphabetical order)　Handbook of Teichmuller Theory　VI　71-94　2017　
  • 　Formule différentielle du longueur extrémale et deux applications (Differential formula of the extremal length and two applications)　Hideki Miyachi, Ken'ichi Ohshika (in alphabetical order)　Annales Mathematiques Blaise Pascal.　24　115-133　2017　
  • 　A rigidity theorem for holomorphic disks in Teichmuller spaces 　Hideki Miyachi　Proceedings of American Mathematical Society　143　2949-2957　2015
  • 　A criterion for holomorphic families of Riemann surfaces to be virtually isomorphic 　Hideki Miyachi　Proceedings of the Japan Academy, Series A, Mathematical Sciences　91　10　151-154　2015
  • 　Extremal length geometry　Hideki Miyachi　Handbook of Teichmuller theory　IV　197-234　2014
  • 　Lipschitz algebra and compactifications of Teichmuller space　Hideki Miyachi　Handbook of Teichmuller theory　IV　375-413　2014
  • 　On extendibility of a map induced by Bers isomorphism　Hideki Miyachi and Toshihiro Nogi　Proc. Amer. Math. Soc.,　142　4181-4189　2014
  • 　Extremal length boundary of Teichmuller space contains non-Busemann points　HIdeki Miyachi　Trans. Amer. Math. Soc.　366　5409-5430　2014
  • 　Unification of the extremal length geometry on Teichmuller space via intersection number　Hideki Miyachi　Mathematische Zeitschrift　278　1065-1095　2014
  • 　Weil-Petersson Funk metric on Teichmuller space　Hideki Miyachi,, Ken’ichi Ohshika, and Sumio Yamada　Handbook of Hilbert geometry　339-352　2014
  • 　Spirals and the asymptotic Teichmuller space　Hideki Miyachi　Computational Methods and Function Theory　14　2　609-622　2014
  • 　Teichmuller rays and the Gardiner-Masur boundary of Teichmuller space II　Hideki Miyachi　Geometriae Dedicata　162　1　283-304　2013
  • 　A Characterization of Biholomorphic Automorphisms of Teichmuller Space　Ryosuke Mineyama, Hideki Miyachi　Mathematical Proceedings of the Cambridge Philosophical Society　154　71-83　2013
  • 　A differential formula for Extremal length　Hideki Miyachi　In the tradition of Ahlfors-Bers, VI, Contemporary mathematics　590　137-152　2013
  • 　Integrations of invariant measures over the moduli space of Riemann surfaces　Hideki Miyachi　Teichmuller Space and Related Topics, Josai Mathematical Monograph　5　39-49　2012
  • 　Uniform weak*-topology and Earthquakes in the hyperbolic plane　Hideki Miyachi, Dragomir Saric　Proceedings of the London Mathematical Society　105　1123-1148　2012
  • 　Holonomies and the slope inequality of Lefschetz fibrations　Hideki Miyachi, Hiroshige Shiga　Proc. Amer. Math. Soc.　139　1299-1307　2011
  • 　Quasiarcs and the outside of the asymptotic Teichmuller space　Hideki Miyachi　Infinite dimensional Teichmuller space and moduli space, RIMS Kôkyûroku Bessatsu　17　85-104　2010
  • 　Uniform models for the closure of the Riley slice　Ken'ichi Ohshika, Hideki Miyachi　In the tradition of Ahlfors-Bers, V, Contemporary mathematics　510　249-306　2010
  • 　The inner and outer radii of asymptotic Teichmuller spaces　Hideki Miyachi　Complex Variables and Elliptic Equations　53　2　139-158　2008
  • 　On the Gardiner-Masur boundary of Teichmuller spaces　Hideki Miyachi　Proceedings of the 15th ICFIDCAA Osaka 2007, OCAMI Studies　2　295-300　2008
  • 　Image of asymptotic Bers Map　Hideki Miyachi　Journal of Mathematical Society of Japan 　60　4　1255-1276　2008
  • 　Teichmuller rays and the Gardiner-Masur boundary of Teichmuller space　Hideki Miyachi　Geometriae Dedicata　137　113-141　2008
  • 　A reduction for asymptotic Teichmuller spaces　Hideki Miyachi　Ann. Acad. Sci. Fenn. Math　32　55-71　2007
  • 　On invariant distances on asymptotic Teichmuller spaces　Hideki Miyachi　Proc. Amer. Math. Soc.　134　7　1917-1925　2006
  • 　Variations of McShane's identity for punctured surface groups　Hirotaka Akiyoshi, Hideki Miyachi, Makoto Sakuma　Spaces of Kleinian groups, LMS Lec.Notes　329　151-185　2005
  • 　Moduli of Continuity of Cannon-Thurston maps　Hideki Miyachi　Spaces of Kleinian groups, LMS Lec.Notes　329　121-149　2005
  • 　On topologically tame Kleinian groups with bounded geometry　Kenichi Ohshika, Hideki Miyach　Spaces of Kleinian groups, LMS Lec.Notes　329　29-48　2005
  • 　The limit sets of quasifuchsian punctured surface groups and the Teichmuller distances　Hideki Miyachi　Kodai Journal of Mathematics　28　301-309　2005
  • 　A refinement of McShane's identity for quasifuchsian punctured torus groups　Hirotaka Akiyoshi, Hideki Miyachi, Makoto Sakuma　In the tradition of Ahlfors and Bers III, Contemporary mathematics　355　21-40　2004
  • 　Cusps in complex boundaries of one-dimensional Teichmuller space　Hideki Miyachi　Conform. Geom. Dyn　7　103-151　2003
  • 　Quasi-arcs in the limit set of a singly degenerate group with bounded geometry　Hideki Miyachi　Kleinian Groups and Hyperbolic 3-Manifolds, LMS. Lec. Notes　299　131-144　2003
  • 　On the horocyclic coordinate for the Teichmuller space of once punctured tori　Hideki Miyachi　Proc. Amer. Math. Soc.　130　1019-1029　2002
  • 　On the existence of certain quadratic differentials on four times punctured spheres and once punctured tori　Hideki Miyachi　Kodai Math. J.　22　187-207　1999
  • 　On the area of the complement of the invariant component of certain b-groups and On sequences of terminal regular b-groups　Hideki Miyachi　J. Math. Kyoto Univ.　39　421-434　1999

Conference Presentations

  • Towards Complex analysis on Teichmueller space(conference：International Conference on Complex Analysis 2019)(2019/09/18)
  • Complex Analysis on Teichmüller space(conference：HAYAMA Symposium on Complex Analysis in Several Variables XXI)(2019/07/13)
  • Poisson integral formula for Teichmueller space (conference：Riemann surfaces and Teichmuller theory)(2019/07/08)
  • Toward Complex analysis on Teichmueller space(conference：Workshop on Holomorphic Maps, Pluripotentials and Complex Geometry)(2019/03/26)
  • Poisson integral formula for Teichmueller space (2019/02/11)

show all

  • Toward Complex analysis on Teichmuller space(2018/12/12)
  • Toward Complex analysis with Thurston's theory (conference：New Trends in Teichmuller Theory and Mapping Class Groups)(2018/09/02)
  • Teichmuller theory and shear coordinates(2018/01/26)
  • Toward complex analysis on Teichmuller space(2017/12/24)
  • Deformation of holomorphic quadratic differentials and its applications(2017/12/19)
  • Extremal length geometry on Teichmuller space(2117/11/15)
  • Deformation of Riemann surfaces via affine deformations(2017/09/16)
  • タイヒミュラー空間論の位相幾何学的側面と複素解析的側面の一意化に向けて(2017/08/21)
  • Towards complex analysis on Teichmüller space with Thurston's theory(conference：Geometry and physics, Dedicated to the memory of W.P.Thurston, 99e rencontre entre mathématiciens et physiciens théoriciens : Géométrie et physique)(2017/07/08)
  • Deformation of singular flat structures from quadratic differentials and Riemann surfaces(conference："Special Session on Geometric Function Theory and Related topics” (SS 19 A) , AMS Meeting #1129)(2017/05/07)
  • On deformations of affine deformations(conference：Mini-workshop``Growth 4")(2017/04/22)
  • Extremal length geometry on Teichmuller space(2017/01/11)
  • Extremal length geometry on Teichmuller space(conference：Symposium on Differential Geometry/Teichmuller theory, in cooperation with American Mathematical Society, International Conference of The Indian Mathematics Consortium, DST-Centre for Interdisciplinary Mathematical Sciences)(2016/12/17)
  • Levi forms of extremal length functions and the period matrices of ramified double coverings(conference：Workshop on Grothendieck-Teichmüller Theories)(2016/07/27)
  • Complex analysis on Teichmuller space with extremal length(conference：Special Session on "Teichmüller Theory and Related Topics" at the AMS Sectional Meeting)(2016/03/20)
  • Levi Form of Extremal Length Functions on Teichmuller Space(conference：Complex Analysis and Dynamics Seminar)(2016/03/18)
  • Towards complex geometry of Teichmuller space(conference：L2 Extension Theorems)(2016/02/17)
  • Towards the complex geometry of Teichmuller space with extremal length (conference：Workshop on Teichmüller Theory and Low-Dimensional Topology at TSIMF)(2016/01/11)
  • Towards the complex geometry of Teichmuller space with extremal length(conference：複素解析幾何セミナー)(2015/11/16)
  • Toward the complex geometry of Teichmuller distance(conference：Topology and Groups)(2015/10/17)
  • Hyperbolic and non-hyperbolic nature of Teichmuller space(conference：Seminar at Mathematics Department)(2015/10/14)
  • Toward the complex geometry of Teichmuller space from extremal length geometry - The Levi form of extremal length functions(conference：French-Japanese workshop on Teichmuller spaces and surface mapping class groups)(2015/06/04)
  • Spirals and the asymptotic Teichmuller space(2015/02/15)
  • Dynamical approach to the infinitesimal spaces of quasiconformal mappings(conference：阪大力学系・フラクタルセミナー)(2015/01/21)
  • Geometry of the Gromov product in Teichmuller theory(conference：Group Action Forum)(2014/12/18)
  • Finsler geometry on Teichmuller metric(conference：The 49-th Symposium on Finsler Geometry)(2014/12/05)
  • 極値的長さの幾何学とその応用(conference：東工大複素解析セミナー)(2014/11/19)
  • Extremal length geometry on Teichmuller space and its application(conference：The Ahlfors-Bers Colloquium VI)(2014/10/23)
  • A rigidity theorem for holomorphic disks in Teichmuller space(conference：Atelier de travail franco-japonais sur la géometrie des groupes modulaires et des espaces de Teichmüller)(2014/10/15)
  • A rigidity theorem for holomorphic disks in Teichmueller space(conference：Séminaire GT3)(2014/09/17)
  • タイヒミュラー空間への正則写像の剛性とその応用(2014/08/28)
  • タイヒミュラー空間の幾何学(conference：広島大学理学研究科数学教室談話会)(2014/07/15)
  • A criterion for virtually isomorphism on holomorphic families of Riemann surfaces(2014/06/06)
  • Rigidity of Holomorphic disks in Teichmuller space(conference：Hyperbolic geometry session, Iberoamerican Congress 2014)(2014/05/22)
  • Rough homotheties on metric spaces(conference：Master class on Finsler geometry and application)(2014/04/10)
  • タイヒミュラー距離の幾何学とその応用(conference：東京大学複素解析幾何セミナー)(2014/01/20)
  • Hyperbolic geometry and Teichmuller theory I, II, III（３回講演）(2014/01/11)

Others

Arts and Fieldwork

Patent

Theme to the desired joint research

Grant-in-Aid for Scientific Research

○「タイヒミュラー空間論の複素解析的側面の深化と多角的視点からの新展開」(2020-2024)　
○「タイヒミュラー空間の複素解析的構造の研究」(2016-2019)　
○「タイヒミュラー空間及びクライン群の変形空間の複素解析的構造の研究」(2009-2014)　
○「タイヒミュラー空間とクライン群の変形空間の複素解析的構造の研究」(2005-2007)　

Competitive research funding,Contribution

Collaborative research,Consignment study

Classes (Bachelors)

○Linear Algebra 1(2018)
○Fundamental Concepts of Mathematics A(2018)
○Fundamental Concepts of Mathematics B(2018)
○Fundamental Concepts of Mathematics A,B(2018)
○Linear Algebra 1(2018)

Classes (Graduate Schools)

International Project

International Students

Lecture themes

Others (Social Activities)

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