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Researcher Information

last modified:2019/02/15

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

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

Specialities

Basic analysis

Speciality Keywords

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

Research Themes

Books

Papers

  •  A dynamical approach to the infinitesimal spaces of quasiconformal mappings Hideki Miyachi Proceedings of American Mathematical Society 147 215-227 2019 
  •  Geometry of the Gromov product: Geometry at infinity of Teichmueller space  Hideki Miyachi Journal of Mathematical Society of Japan 69 995-1049 2017
  •  Extremal length functions are log-plurisubharmonic  Hideki Miyachi Tradition of Ahlfors–Bers, VII, Contemporary mathematics 696 225-250 2017
  •  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 

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  •  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
  •  Lipschitz algebra and compactifications of Teichmuller space Hideki Miyachi Handbook of Teichmuller theory IV 375-413 2014
  •  Extremal length geometry Hideki Miyachi Handbook of Teichmuller theory IV 197-234 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
  •  Uniform weak*-topology and Earthquakes in the hyperbolic plane Hideki Miyachi, Dragomir Saric Proceedings of the London Mathematical Society 105 1123-1148 2012
  •  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
  •  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

  • 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)

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  • 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)

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の複素解析的構造の研究」(2016-2020) 
○「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) 

Classes (Bachelors)

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

Classes (Graduate Schools)

○Topics in Mathematical Science Ia(2018)

International Project

International Students

Lecture themes

Others (Social Activities)

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