Prof. Martin Man Chun LI

Associate Professor
BSc (The Chinese University of Hong Kong)
PhD (Stanford University)

Prof. Martin Man Chun LI

Room 236, Lady Shaw Building,
The Chinese University of Hong Kong,
Shatin, N.T., Hong Kong

(852) 3943 1851

Fields of Interest:
Geometric Analysis, Geometric Partial Differential Equations, General Relativity

Selected Publications:
  1. A maximum principle for free boundary minimal varieties of arbitrary codimension (joint work with X. Zhou)
    Comm. Anal. Geom. 29 (2021), no. 6, 1509-1521
  2. Free boundary minimal surfaces in the unit three-ball via desingularization of the critical catenoid and the equatorial disk (joint work with N. Kapouleas)
    J. Reine Angew. Math. 776 (2021), 201-254
  3. Min-max theory for free boundary minimal hypersurfaces I: regularity theory (joint work with X. Zhou)
    J. Differential Geom. 118 (2021), no.3, 487-553
  4. Min-max theory for free boundary minimal hypersurfaces II: general Morse index bounds and applications (joint work with Q. Guang, Z. Wang and X. Zhou)
    Math. Ann. 379 (2021), 1395-1424
  5. Curvature estimates for stable free boundary minimal hypersurfaces (joint work with Q. Guang and X. Zhou)
    J. Reine Angew. Math. 759 (2020), 245-264
  6. Chord shortening flow and a theorem of Lusternik and Schnirelmann
    Pacific Journal of Math. 299 (2019), no. 2, 469-488
  7. Free boundary minimal surfaces in the unit ball: recent advances and open questions
    Proceedings of the International Consortium of Chinese Mathematicians, 2017 (First Annual Meeting), p.401-436, International Press of Boston, Inc. (2020) 654pp.
  8. A general existence theorem of embedded minimal surfaces with free boundary
    Comm. Pure Appl. Math. 68 (2015), no. 2, 286-331
  9. A sharp comparison theorem for compact manifolds with mean convex boundary
    J. Geom. Anal. 24 (2014), no. 3, 1490-1496
  10. Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary (joint work with A. Fraser)
    J. Differential Geom. 96 (2014), no. 2, 183-200

Major Research Grants:
  • National Natural Science Foundation of China (優青項目)
  • Research Grants Council - General Research Fund

Honours and Awards:
  • Hong Kong Mathematical Society Young Scholar Award
  • Faculty Exemplary Teaching Award


Course Code Course Title Academic Year Term
MATH2028 Honours Advanced Calculus II 2023/24 1
MATH2050B Mathematical Analysis I 2023/24 1
MATH5061 Riemannian Geometry I 2023/24 2