Research interests
My research focuses on fully nonlinear elliptic equations and geometric analysis, particularly the convexity and regularity of solutions to real and complex Monge–Ampère equations, $k$-Hessian equations, and special Lagrangian equations. Recently, my focus has been on convexity problems for solutions on manifolds and classification problems for elliptic equations.
Education
- 2025.09 – Present Ph.D. in Mathematics · Lanzhou University
- 2020.09 – 2023.06 M.S. in Mathematics · Lanzhou University
- 2015.09 – 2019.06 B.S. in Mathematics · Yunnan University Dianchi College
Publications
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Power convexity of solutions to a special Lagrangian equation in dimension two.
Preprints
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Classification of entire concave solutions to semilinear elliptic equations.
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A strong constant rank theorem for semilinear elliptic equations.
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Power convexity of the torsion function on horo-convex domains in hyperbolic space.
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Power convexity of solutions to complex Monge–Ampère equation in $\mathbb{C}^2$.
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The log-concavity of eigenfunction to complex Monge–Ampère operator in $\mathbb{C}^2$.
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A Liouville theorem for the 2-Hessian equation on the Heisenberg group.
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The constant rank theorem for complex Lagrangian phase operator.
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On the constant rank theorem for special Lagrangian type operator on $\mathbb{S}^n$.
Notes
- Lecture notes on minimal surfaces
- 椭圆方程积分恒等式的应用 (in Chinese)
- Master’s thesis — 二维 special Lagrangian 方程解的幂凸性 (in Chinese)