关注超曲面几何与拉格朗日子流形的微分几何相关问题。用可积系统方法研究了复射影平面中极小拉格朗日曲面的构造；系统研究了复二次超曲面中的拉格朗日子流形几何与球 面中超曲面几何的关系，得到了球面中所有齐性等参超曲面的高斯映射像的哈密顿稳定性和大部分高斯映射像的 Floer 同调；得到了欧氏空间中 sigma_k^alpha 曲率流的紧致强凸自相似解的唯一性及欧氏空间中常异向平均曲率超曲面的 Alexandrov 型定理等。
代表作：
[1] Josef F. Dorfmeister and Hui Ma, Minimal Lagrangian surfaces in CP^2 via the loop group method part II: The general case, Journal of Geometry and Physics, 209 (2025), Paper No. 105398, 35 pp.
[2] Hui Ma and Jing Wu, Sobolev inequalities in manifolds with nonnegative intermediate Ricci curvature, J. Geom. Anal. 34 (2024), no. 3, Paper No. 93, 16 pp.
[3] Shanze Gao, Hui Ma and Mingxuan Yang, Overdetermined problems for fully nonlinear equations with constant Dirichlet boundary conditions in space forms, Calc. Var. Partial Differential Equations 62 (2023), no. 6, Paper No. 183, 19 pp.
[4] Josef F. Dorfmeister and Hui Ma, Minimal Lagrangian surfaces in CP^2 via the loop group method Part I: The contractible case, Journal of Geometry and Physics, 161 (2021), Paper No. 104016, 27 pp.
[5] Shanze Gao, Haizhong Li and Hui Ma, Uniqueness if closed self-similar solutions to σ^k_α-curvature flow, Nonlinear Differential Equations Appl. 25 (2018), no. 5, Art.45, 26pp.
[6] Hiroshi Iriyeh, Hui Ma, Reiko Miyaoka and Yoshihiro Ohnita, Hamiltonian non-displaceability of Gauss images of isoparametric hypersurfaces, Bull. London Math. Soc. 48 (2016), 802--812.
[7] Hui Ma and Yoshihiro Ohnita, Homogeneous stability of the Gauss images of homogeneous isoparametric hypersurfaces II, Tohoku Math J. (2) 67 (2015), no.2, 195–246.
[8] Hui Ma and Yoshihiro Ohnita, Homogeneous stability of the Gauss images of homogeneous isoparametric hypersurfaces I, J. Diff. Geom. 97(2014), 275-348.
[9] Yijun He, Haizhong Li, Hui Ma and Jianquan Ge, Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures, Indiana Univ. Math. J. 58 (2009), no. 2, 853-868.
[10] Hui Ma and Yoshihiro Ohnita, On Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres, Math. Z. 261 (2009), 749-785.
[11] Hui Ma, Hamiltonian stationary Lagrangian surfaces in CP^2, Ann. Global Anal. Geom. 27 (2005), no. 1, 1-16.
