Martin Li

Publications

Journal 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 journal link 
2. 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 journal link 
3. 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 journal link
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  journal link
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 journal link 
6. Chord shortening flow and a theorem of Lusternik and Schnirelmann
   Pacific Journal of Math. 299 (2019), no. 2, 469-488 journal link
7. A general existence theorem of embedded minimal surfaces with free boundary
   Comm. Pure Appl. Math. 68 (2015), no. 2, 286-331 journal link
   
8. 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 journal link
   
9. A sharp comparison theorem for compact manifolds with mean convex boundary
   J. Geom. Anal. 24 (2014), no. 3, 1490-1496 journal link
   
10. On complete stable minimal surfaces in 4-manifolds with positive isotropic curvature
    Proc. Amer. Math. Soc. 140 (2012), 2843-2854 journal link
    

Preprints

1. Contracting convex surfaces by mean curvature flow with free boundary on convex barriers (joint work with S. Hirsch)
   submitted arXiv preprint

Research reports and surveys

1. 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. arXiv preprint
2. On minimal surfaces with free boundary (joint work with X. Zhou)