### Research Focus

Geometric Analysis and Calculus of Variations

### Publications

1. Generic scarring for minimal hypersurfaces along stable hypersurfaces (with A. Song), *Geom. Funct. Anal.* (2021), to appear, arXiv:2006.03038.

2. On the Multiplicity One Conjecture in min-max theory, *Ann. of Math.* (2) 192 (2020), no. 3, 767-820.

3. Existence of hypersurfaces with prescribed mean curvature I - Generic min-max (with J. Zhu), *Camb. J. Math.* 8 (2020), no. 2, 311-362.

4. Min-max minimal disks with free boundary in Riemannian manifolds, (with L. Lin and A. Sun), *Geom. Topol. *24 (2020), no. 1, 471-532.

5. Min-max theory for constant mean curvature hypersurfaces, (with J. Zhu), Invent. Math. 218 (2019), no. 2, 441-490.

6. Min-max theory for free boundary minimal hypersurfaces I: regularity, (with M. Li), *J. Differential Geom.*, to appear, arXiv:1611.02612.

7. Curvature estimates for stable minimal hypersurfaces with free boundary, (with Q. Guang and M. Li), *J. Reine Angew. Math.* 759 (2020), 245-264.

8. Entropy of closed surfaces and min-max theory, (with D. Ketover), *J. Differential Geom.* 110 (2018), no. 1, 31-71.

9. Min-max hypersurface in manifold of positive Ricci curvature,* J. Differential Geom. *105 (2017), no. 2, 291-343.

10. Min-max minimal hypersurface in (Mn+1, g) with Ricg > 0 and 2 ≤ n ≤ 6, *J. Differential Geom.* 100 (2015), no. 1, 129-160.

11. Convexity of reduced energy and mass angular momentum inequalities, (with R. Schoen), *Ann. Henri Poincaré* 14 (2013), no. 7, 1747-1773.

12. On the existence of min-max minimal surfaces of genus g ≥ 2, *Commun. Contemp. Math.* 19 (2017), no. 4, 1750041, 36 pp.

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