Xin Zhou

Associate Professor

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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Courses - Fall 2022

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