About Me
I am currently a Ph.D. student in Mathematics at The Chinese University of Hong Kong, under the supervision of Professor Juncheng Wei.
Education
Personal Awards
Curriculum Vitae
You can view and download my complete CV here: Qian Zhenye's CV (PDF)
Research
Research Interests
My research lies at the interface of nonlinear elliptic partial differential equations, geometric analysis, and the calculus of variations. I am broadly interested in geometric variational problems and rigidity and classification questions for nonlinear PDEs. Current directions include harmonic maps and related problems appearing in Brezis' open problems, as well as Allen–Cahn and fractional Allen–Cahn equations and their connections with minimal and nonlocal minimal surfaces. A recurring theme in my work is how variational structure, stability, topology, and geometry constrain the existence and qualitative behavior of solutions.
Keywords: Nonlinear elliptic PDEs · Geometric analysis · Harmonic maps · Allen–Cahn equations · Minimal surfaces · Rigidity and Liouville problems
Research Projects
Brezis' Open Problems and Geometric Variational Problems
I am interested in longstanding open problems in geometric analysis and the calculus of variations, especially those related to harmonic maps, multiplicity, symmetry, regularity, and continuous harmonic extensions highlighted by Brezis, as well as related critical elliptic problems.
Allen–Cahn Equations, Phase Transitions, and Minimal Surfaces
I study Allen–Cahn equations and their fractional/nonlocal counterparts, with connections to phase transition phenomena, minimal surfaces, nonlocal minimal surfaces, and De Giorgi– and Bernstein-type conjectures.
Rigidity, Liouville Theorems, and Classification Problems
A central theme is the classification and rigidity of entire solutions to semilinear and nonlocal elliptic equations, exploring how stability, topology, variational structure, and geometric information determine qualitative behavior.
Preprints
Publications
Selected Talks
December 2025 — Phase transition, Minimal surfaces and De Giorgi conjecture
2025 Global Riemannian Geometry Seminar (Fall and Winter Semester)
Zhejiang University, Zhejiang, China
August 2024 — The geometric topology of frontal surfaces
2024 International Workshop on Geometry, Topology of Singular Submanifolds and Related Topics
Northeast Normal University, Jilin, China
Academic Activities
Summer Schools and Workshops
July 2026 — University of Science and Technology of China: Summer School on Partial Differential Equations
June 2026 — XMU Tianyuan Mathematical Center in Southeast China: Summer School on Differential Geometry
January 2026 — Academy of Mathematics and Systems Science, Chinese Academy of Sciences: Geometric Partial Differential Equations Conference
July 2025 — USTC Institute of Geometry and Physics: Summer School in Geometry and Analysis
June 2025 — Zhejiang University: Partial Differential Equation Advanced Workshop
August 2024 — Peking University BICMR: Summer School on Differential Geometry
July 2024 — USTC Institute of Geometry and Physics: Summer School in Geometry
Seminars and Conferences
September 2025 - January 2026 — Elliptic Partial Differential Equations Seminar
Sunday 14:00-17:00, Room 101, Building 2, Hainayuan, Zhejiang University (School of Mathematical Sciences)
with H.J. Chen (ZJU), Z.J. Hu (ZJU), M.T. Zhu (WU), T.Y. Shen (ShanghaiTech), T.L. Wang (AMSS)
June 2025 - present — PDE & Geometric Analysis Seminar (Online)
An online discussion seminar focusing on partial differential equations, geometric analysis, calculus of variations, and related topics.
Selected talks and records: Bilibili records
June 2025 - present — Minimal Surfaces Seminar (online) - selected videos
The whole talks:
- 6.24 — A simple survey of minimal surfaces and related aspects (Zhenye Qian, HZNU)
- 7.5 — The minimal surfaces equation and minimal submanifolds (Haoyu Pan, HZNU)
- 7.18 — Applications of the first variation and Bernstein problem in two dimensions (Tian Zeng, CQU)
- 8.1 — The second Variation formula and Stability (Tian Zeng, CQU)
- 8.8 — Bernstein problem I: The fundamental objects of Geometric Measure Theory (Mutian Zhu, WU)
- 8.15 — Bernstein problem II: Regularity theory in Geometric Measure Theory (Mutian Zhu, WU)
- 8.22 — Bernstein problem II (cont.): Regularity theory in Geometric Measure Theory (Mutian Zhu, WU)
- 8.28 — Bernstein problem III: Bernstein problem and Simons cone (Mutian Zhu, WU)
- 10.10 — Small Energy Curvature Estimates for Minimal Surfaces (Weipeng Ruan, XMU)
- 10.17 — Extension of Schoen-Simon-Yau via De Giorgi iteration (Bellettini 2025) (Weipeng Ruan, XMU)
August 2024 - March 2025 — Riemannian Geometry and Geometry Analysis, Hangzhou Normal University - selected videos
Selected topics I have talked:
- Riemannian Submanifold and Basic Equations, some aspects in Minimal Submanifolds in Euclidean space
- Comparison theorem in Riemannian Geometry (Rauch, Hessian and Laplacian, Volume)
- Cheeger–Gromov convergence and Gromov's precompactness theorem with some applications in lower bound Ricci curvature
- Bochner Technique on Riemannian Geometry and applications (Comparison theorems, Killing fields)
- Some aspects in CMC hypersurfaces: Alexandrov's theorem, Lévy–Gromov Isoperimetric inequality
- Bernstein's theorem in Minimal surfaces and Plateau problem
August 2024 - December 2024 — Algebraic Topology, Hangzhou Normal University
Selected topics I have talked:
- An Introduction to Cohomology Ring: Universal coefficient theorem, Cup product and Examples
- Some Applications of Mayer–Vietoris Argument: Künneth formula, Leray–Hirsch theorem in fiber bundle, Poincaré's duality for manifolds
- Some aspects in homotopy theory: Freudenthal suspension and introduction to stable homotopy groups, Hurewicz–Whitehead theorem and Motivation in Poincaré's Conjecture of 3-dim manifolds
Teaching
Teaching Assistant Experience
Autumn 2025 — Analytic Geometry, Hangzhou Normal University (joint with Tianyi Shen)
Instructor: Zhiyuan Xu
Spring 2025 — Differential Geometry (Honor), Hangzhou Normal University
Instructor: Zhiyuan Xu
References: exercises and supplementary materials
Autumn 2024 — Analytic Geometry, Hangzhou Normal University
Instructor: Zhiyuan Xu
References: exercises and supplementary materials
Notes
Links
- Google Scholar: Zhenye QIAN
- Study vlogs: Bilibili
- Ideas and discussions: Zhihu