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 | 2022/23 | 1 |
| MATH2050C | Mathematical Analysis I | 2022/23 | 2 |
| MATH6022B | Topics in Geometry II | 2022/23 | 2 |
| Course Code | Course Title | Academic Year | Term |
|---|---|---|---|
| MATH2028 | Honours Advanced Calculus II | 2021/22 | 1 |
| MATH2050C | Mathematical Analysis I | 2021/22 | 2 |
| MATH6022B | Topics in Geometry II | 2021/22 | 2 |
| MATH6021 | Topics in Geometry I | 2020/21 | 1 |
| MATH2050C | Mathematical Analysis I | 2020/21 | 2 |
| MATH5061 | Riemannian Geometry I | 2020/21 | 2 |
| MATH4030 | Differential Geometry | 2019/20 | 1 |
| MATH2050C | Mathematical Analysis I | 2019/20 | 2 |
| MATH5061 | Riemannian Geometry I | 2019/20 | 2 |
| MATH2050C | Mathematical Analysis I | 2018/19 | 2 |
| MATH2040A | Linear Algebra II | 2017/18 | 1 |
| MATH4030 | Differential Geometry | 2017/18 | 1 |
| MATH1030F | Linear Algebra I | 2017/18 | 2 |
| MATH2040A | Linear Algebra II | 2016/17 | 1 |
| MATH4030 | Differential Geometry | 2016/17 | 1 |
| MATH1030F | Linear Algebra I | 2016/17 | 2 |
| MATH4030 | Differential Geometry | 2015/16 | 1 |
| MATH2040A | Linear Algebra II | 2015/16 | 2 |
| MATH1010E | University Mathematics | 2014/15 | 1 |
| MATH2010B | Advanced Calculus I | 2014/15 | 1 |