Prof. Martin Man Chun LI

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


Prof. Martin Man Chun LI
ORCID:
0000-0002-1877-9409

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

Tel:
(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

Professional activities:

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Courses