# Prof. Martin Man Chun LI

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

**ORCID:**

0000-0002-1877-9409

**Address:**

Room 236, Lady Shaw Building,

The Chinese University of Hong Kong,

Shatin, N.T., Hong Kong

The Chinese University of Hong Kong,

Shatin, N.T., Hong Kong

**Tel:**

(852) 3943 1851

**Email:**

**Personal Website:**

**Fields of Interest:**

Geometric Analysis, Geometric Partial Differential Equations, General Relativity

**Selected Publications:**

- 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 - 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 - 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 - 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 - Curvature estimates for stable free boundary minimal hypersurfaces (joint work with Q. Guang and X. Zhou)

J. Reine Angew. Math. 759 (2020), 245-264 - Chord shortening flow and a theorem of Lusternik and Schnirelmann

Pacific Journal of Math. 299 (2019), no. 2, 469-488 - 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. - A general existence theorem of embedded minimal surfaces with free boundary

Comm. Pure Appl. Math. 68 (2015), no. 2, 286-331 - A sharp comparison theorem for compact manifolds with mean convex boundary

J. Geom. Anal. 24 (2014), no. 3, 1490-1496 - 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

#### Courses

Course Code | Course Title | Academic Year | Term |
---|---|---|---|

MATH2028 | Honours Advanced Calculus II | 2023/24 | 1 |

MATH2050B | Mathematical Analysis I | 2023/24 | 1 |