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Geometric Analysis; Calculus of Variations; General Relativity
- MATH 4140 : Honors Introduction to Analysis II
- MATH 4900 : Supervised Research
- MATH 4901 : Supervised Reading
- MATH 6620 : Riemannian Geometry
- Existence of hypersurfaces with prescribed mean curvature I - Generic min-max (with J. Zhu), accepted by Cambridge Journal of Mathematics, arXiv:1808.03527.
- Min-max minimal disks with free boundary in Riemannian manifolds, (with L. Lin and A. Sun), accepted by Geometry & Topology, arXiv:1806.04664.
- Min-max theory for constant mean curvature hypersurfaces, (with J. Zhu), Invent. math. (2019) 218:441–490.
- Min-max theory for free boundary minimal hypersurfaces I: regularity, (with M. Li), accepted by J. of Differential Geom., arXiv:1611.02612.
- A maximum principle for free boundary minimal varieties of arbitrary codimension, (with M. Li), accepted by Comm. Anal. Geom., arXiv:1708.05001.
- Curvature estimates for stable minimal hypersurfaces with free boundary, (with Q. Guang and M. Li), accepted by J. Reine Angew. Math (Crelle’s Journal), DOI: https://doi.org/10.1515/crelle-2018-0008.
- Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces, (with Y. Liokumovich), Int. Math. Res. Not. IMRN 2018, no. 4, 1129-1152.
- Entropy of closed surfaces and min-max theory, (with D. Ketover), J. Differential Geom. 110 (2018), no. 1, 31-71.
- Existence of minimal surfaces of arbitrary large Morse index, (with H. Li), Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 64, 12 pp.
- Min-max hypersurface in manifold of positive Ricci curvature, J. Differential Geom. 105 (2017), no. 2, 291-343.
- On the free boundary min-max geodesics, Int. Math. Res. Not. IMRN 2016, no. 5, 1447-1466.
- Min-max minimal hypersurface in (Mn+1,g) with Ricg > 0 and 2 ≤ n ≤ 6, J. Differential Geom. 100 (2015), no. 1, 129-160.
- Mass angular momentum inequality for axisymmetric vacuum data with small trace, Comm. Anal. Geom. 22 (2014), no. 3, 519-571.
- Convexity of reduced energy and mass angular momentum inequalities, (with R. Schoen), Ann. Henri Poincar´ e 14 (2013), no. 7, 1747-1773.
- On the existence of min-max minimal surfaces of genus g ≥ 2, Commun. Contemp. Math. 19 (2017), no. 4, 1750041, 36 pp.
- On the existence of min-max minimal torus, J. Geom. Anal. 20 (2010), no. 4, 1026-1055.