ZHOU Xiaodan ＺＨＯＵＸｉａｏｄａｎ

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Zhou Xiaodan ZHOU Xiaodan

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Researcher Number	10871494
Other IDs
Affiliation (Current)	2026: 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	2020 – 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
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 / Metric measure spaces / Sobolev mappings / Absolute Continuity / Poincare inequality / Newton-Sobolev mapping … More / Quasiconformal mapping / p-Laplace / Green function / PI spaces / non-local functional / nonlocal functional / BV functions / Lusin property / Sobolev functions / weighted spaces / Quasiconformal mappings / 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

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 2025 2024 2023 2022 2021 2020

All Journal Article Presentation

[Journal Article] A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow2025
- Author(s)
  Kijowski Antoni、Liu Qing、Zhang Ye、Zhou Xiaodan
- Journal Title
  
  Discrete and Continuous Dynamical Systems
  
  Volume: 45 Issue: 9 Pages: 3483-3511
- DOI
  10.3934/dcds.2025029
- Peer Reviewed
- Data Source
  KAKENHI-PROJECT-22K13947, KAKENHI-PROJECT-22K03396
[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] BV Functions and Nonlocal Functionals in Metric Measure Spaces2024
- Author(s)
  Lahti Panu、Pinamonti Andrea、Zhou Xiaodan
- Journal Title
  
  The Journal of Geometric Analysis
  
  Volume: 34 Issue: 10 Pages: 318-318
- DOI
  10.1007/s12220-024-01766-8
- 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] Uniqueness of Green functions in metric spaces, yes and no2024
- Author(s)
  Xiaodan Zhou
- Organizer
  Analysis seminar, University of Cincinnati 2024
- Invited
- Data Source
  KAKENHI-PROJECT-22K13947
[Presentation] Uniqueness of Green functions in metric spaces, yes and no2024
- Author(s)
  Xiaodan Zhou
- Organizer
  Keio University Nonlinear Analysis Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-22K13947
[Presentation] Green functions on metric spaces2024
- Author(s)
  Xiaodan Zhou
- Organizer
  University of Cincinnati Analysis Seminar
- Invited
- Data Source
  KAKENHI-PROJECT-22K13947
[Presentation] Superposition of subsolutions to infinite Laplace equation in disjoint variables2024
- Author(s)
  Xiaodan Zhou
- Organizer
  AMS-UMI International joint meeting 2024
- Invited / Int'l Joint Research
- 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-22K13947
[Presentation] Uniqueness of Green functions in metric spaces, yes and no2024
- Author(s)
  Xiaodan Zhou
- Organizer
  RIMS workshop "Harmonic Analysis and Nonlinear Partial Differential Equations"
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K13947
[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] Uniqueness of Green functions in metric spaces, yes and no2024
- Author(s)
  Xiaodan Zhou
- Organizer
  Mini-Workshop on Geometric Variational Problems, Geometric Measure Theory, and Related Topics
- Invited / Int'l Joint Research
- Data Source
  KAKENHI-PROJECT-22K13947
[Presentation] Solving an equation in a space without directions2024
- Author(s)
  Xiaodan Zhou
- Organizer
  Smith college Math Department Thursday Lunch Talk
- Invited
- Data Source
  KAKENHI-PROJECT-22K13947
[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

ZHOU Xiaodan ＺＨＯＵ Ｘｉａｏｄａｎ

Zhou Xiaodan ZHOU Xiaodan

Research Projects

Research Products

Co-Researchers

Nonlinear potential theory on metric spacesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Quasiconformal and Sobolev mappings on metric measure spacesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

Hamilton-Jacobi equations on metric measure spacesPrincipal Investigator

Principal Investigator

Project Period (FY)

Research Category

Review Section

Research Institution

[Journal Article] A second-order operator for horizontal quasiconvexity in the Heisenberg group and application to convexity preserving for horizontal curvature flow2025

Author(s)

Journal Title

DOI

Data Source

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

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Metric quasiconformality and Sobolev regularity in non-Ahlfors regular spaces2024

Author(s)

Journal Title

Data Source

[Journal Article] BV Functions and Nonlocal Functionals in Metric Measure Spaces2024

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Quasiconformal and Sobolev mappings in non-Ahlfors regular metric spaces2024

Author(s)

Journal Title

Data Source

[Journal Article] Horizontally quasiconvex envelope in the Heisenberg group2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Absolutely continuous mappings on doubling metric measure spaces2023

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Differential games and Hamilton-Jacobi-Isaacs equations in metric spaces2022

Author(s)

Journal Title

Data Source

[Journal Article] Equivalence of solutions of eikonal equation in metric spaces2021

Author(s)

Journal Title

DOI

Data Source

[Journal Article] Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations2021

Author(s)

Journal Title

DOI

Data Source

[Presentation] Uniqueness of Green functions in metric spaces, yes and no2024

Author(s)

Organizer

Data Source

[Presentation] Uniqueness of Green functions in metric spaces, yes and no2024

Author(s)

Organizer

Data Source

[Presentation] Green functions on metric spaces2024

Author(s)

ZHOU Xiaodan ＺＨＯＵＸｉａｏｄａｎ