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ZHOU Xiaodan  ZHOU Xiaodan

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Zhou Xiaodan  ZHOU Xiaodan

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Researcher Number 10871494
Other IDs
Affiliation (Current) 2025: 沖縄科学技術大学院大学, 距離空間上の解析ユニット, 准教授
Affiliation (based on the past Project Information) *help 2025: 沖縄科学技術大学院大学, 距離空間上の解析ユニット, 准教授
2020 – 2023: 沖縄科学技術大学院大学, 距離空間上の解析ユニット, 准教授
Review Section/Research Field
Principal Investigator
Basic Section 12020:Mathematical analysis-related / 0201:Algebra, geometry, analysis, applied mathematics,and related fields
Keywords
Principal Investigator
metric measure spaces / potential theory / p-harmonic / Sobolev mapping / Nonlocal functional / Lusin property / Quasiconformal mappings / Metric measure spaces / Sobolev mappings / Absolute Continuity … More / Poincare inequality / nonlocal functional / Newton-Sobolev mapping / Quasiconformal mapping / well-posedness / HJ equations / viscosity solutions / Hamilton-Jacobi equation / h-quasiconvexity / metric measure space / h-quasiconvex functions / discontinuous data / eikonal equation / convexity / differential games / Heisenberg group / metric spaces / viscosity solution / Eikonal equation Less
  • Research Projects

    (3 results)
  • Research Products

    (24 results)
  • Co-Researchers

    (1 People)
  •  Nonlinear potential theory on metric spacesPrincipal Investigator

    • Principal Investigator
      ZHOU Xiaodan
    • Project Period (FY)
      2025 – 2027
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Okinawa Institute of Science and Technology Graduate University
  •  Quasiconformal and Sobolev mappings on metric measure spacesPrincipal Investigator

    • Principal Investigator
      ZHOU Xiaodan
    • Project Period (FY)
      2022 – 2024
    • Research Category
      Grant-in-Aid for Early-Career Scientists
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Okinawa Institute of Science and Technology Graduate University
  •  Hamilton-Jacobi equations on metric measure spacesPrincipal Investigator

    • Principal Investigator
      Zhou Xiaodan
    • Project Period (FY)
      2020 – 2023
    • Research Category
      Grant-in-Aid for Research Activity Start-up
    • Review Section
      0201:Algebra, geometry, analysis, applied mathematics,and related fields
    • Research Institution
      Okinawa Institute of Science and Technology Graduate University

All 2024 2023 2022 2021 2020

All Journal Article Presentation

  • [Journal Article] A characterization of BV and Sobolev functions via nonlocal functionals in metric spaces2024

    • Author(s)
      Lahti Panu、Pinamonti Andrea、Zhou Xiaodan
    • Journal Title

      Nonlinear Analysis

      Volume: 241 Pages: 113467-113467

    • DOI

      10.1016/j.na.2023.113467

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Journal Article] Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces2024

    • Author(s)
      Panu Lahti and Xiaodan Zhou
    • Journal Title

      Analysis and Geometry in Metric Spaces

      Volume: In press

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Journal Article] Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces2024

    • Author(s)
      Panu Lahti and Xiaodan Zhou
    • Journal Title

      Tohoku Mathematical Journal

      Volume: In press

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Journal Article] Horizontally quasiconvex envelope in the Heisenberg group2023

    • Author(s)
      Kijowski Antoni、Liu Qing、Zhou Xiaodan
    • Journal Title

      Revista Matematica Iberoamericana

      Volume: in press Issue: 1 Pages: 57-92

    • DOI

      10.4171/rmi/1417

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K22315, KAKENHI-PROJECT-19K03574
  • [Journal Article] Absolutely continuous mappings on doubling metric measure spaces2023

    • Author(s)
      Lahti Panu、Zhou Xiaodan
    • Journal Title

      manuscripta mathematica

      Volume: in press Issue: 1-2 Pages: 1-21

    • DOI

      10.1007/s00229-023-01460-z

    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Journal Article] Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces2022

    • Author(s)
      Qing Liu and Xiaodan Zhou
    • Journal Title

      Minimax Theory and its Applications

      Volume: in press

    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Journal Article] Equivalence of solutions of eikonal equation in metric spaces2021

    • Author(s)
      Qing Liu, Nageswari Shanmugalingam, Zhou Xiaodan
    • Journal Title

      Journal of Differential Equations

      Volume: 272 Pages: 979-1014

    • DOI

      10.1016/j.jde.2020.10.018

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K03574, KAKENHI-PROJECT-20K22315
  • [Journal Article] Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations2021

    • Author(s)
      Liu Qing、Zhou Xiaodan
    • Journal Title

      ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE

      Volume: XXII Pages: 30-30

    • DOI

      10.2422/2036-2145.201907_001

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-20K22315, KAKENHI-PROJECT-19K03574
  • [Presentation] Green functions on metric spaces2024

    • Author(s)
      Xiaodan Zhou
    • Organizer
      University of Cincinnati Analysis Seminar
    • Invited
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Presentation] Eikonal equations in metric spaces2024

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Smith College Undergraduate seminar
    • Invited
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Discontinuous eikonal equations in metric measure spaces2024

    • Author(s)
      Xiaodan Zhou
    • Organizer
      AMS Spring Eastern Sectional Meeting
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Discontinuous eikonal equations in metric measure spaces2023

    • Author(s)
      Xiaodan Zhou
    • Organizer
      OIST Workshop Geometric Aspects of Partial Differential Equations
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Hamilton-Jacobi equations in metric measure spaces2023

    • Author(s)
      Xiaodan Zhou
    • Organizer
      OIST Analysis and Partial Differential Equations Summer School
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Green functions on metric spaces2023

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Shandong University Research Center for Mathematics and Interdisiciplinary Sciences Seminar
    • Invited
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Presentation] Green functions in metric measure spaces2022

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Probability and Geometry, Osaka University, February 14-16, 2023
    • Data Source
      KAKENHI-PROJECT-22K13947
  • [Presentation] Discontinuous eikonal equations in metric measure spaces2022

    • Author(s)
      Xiaodan Zhou
    • Organizer
      MATRIX-RIMS Tandem Workshop on Geometric Analysis in Harmonic Analysis and PDE
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Horizontally quasiconvex envelope in the Heisenberg group2022

    • Author(s)
      Xiaodan Zhou
    • Organizer
      The 47th Sapporo Symposium on Partial Differential Equations
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Eikonal equations on metric measure spaces2022

    • Author(s)
      Xiaodan Zhou
    • Organizer
      RIMS Women in Mathematics
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Characterization of horizontal quasiconvexity in the Heisenberg group and applications2022

    • Author(s)
      Xiaodan Zhou
    • Organizer
      PDE and Analysis Seminar, University of Pittsburgh
    • Invited
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Horizontal quasiconvex envelope in the Heisenberg group2021

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Himeji conference of Partial Differential Equation
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Horizontally quasiconvex envelope in the Heisenberg group2021

    • Author(s)
      Xiaodan Zhou
    • Organizer
      PDE seminar of HKST
    • Invited
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Horizontally quasiconvex envelope in the Heisenberg group2021

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Geometric and functional inequalities and applications seminar
    • Invited
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Horizontal convex envelope in the Heisenberg group2020

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Chinese Academy of Sciences seminar
    • Invited
    • Data Source
      KAKENHI-PROJECT-20K22315
  • [Presentation] Eikonal Equations on Metric Spaces2020

    • Author(s)
      Xiaodan Zhou
    • Organizer
      Partial Differential Equations under Various Metrics
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-20K22315
  • 1.  柳 青
    # of Collaborated Projects: 0 results
    # of Collaborated Products: 1 results

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