Xin Zhou

Assistant Professor

Address: Department of Mathematics
               South Hall, Room 6501
               University of California Santa Barbara
               Santa Barbara, California 93106 USA
E-mail:   zhou "at" math.ucsb.edu

Current Teaching: Math 241A: Topics in Differential Geometry,   Math 117: Methods of Analysis.

I am organizing the UCSB Differential Geometry Seminar.

I am a member of the Geometry group. Before moving to UCSB, I was a CLE Moore instructor in the Math department at MIT. I received my PhD from Stanford University in 2013 with Richard M. Schoen as my advisor. Here is my Curriculum Vitae.

Research Interest:

Preprints:

  1. Min-max via minimal filling I: three manifold (with S. T. Yau), preprint.
  2. Curvature estimates and compactness for improper minimal hypersurfaces (with Qiang Guang), preprint.
  3. Min-max theory for CMC hypersurfaces (with Jonathan Zhu), arXiv:1707.08012.
  4. A maximum principle for free boundary minimal varieties of arbitrary codimension (with Martin Li), arXiv:1708.05001.
  5. Min-max theory for free boundary minimal hypersurfaces I - regularity theory (with Martin Li), arXiv:1611.02612.
  6. Curvature estimates for stable free boundary minimal hypersurfaces (with Qiang Guang and Martin Li), arXiv:1611.02605.

Publications:

  1. Sweeping out 3-manifold of positive Ricci curvature by short 1-cycles via estimates of min-max surfaces (with Y. Liokumovich), International Mathematics Research Notices. arXiv:1510.02896v1.
  2. Entropy of closed surfaces and min-max theory (with D. Ketover), accepted by J. Differential Geometry, arXiv:1509.06238.
  3. Existence of minimal surfaces of arbitrarily large Morse index (with Haozhao. Li), Calculus of Variations and Partial Differential Equations, 2016, 55(3), 1-12.
  4. Min-max hypersurface in manifold of positive Ricci curvature, J. Differential Geometry, 105 (2017), 291-343.
  5. On the free boundary min-max geodesics, International Mathematics Research Notices Vol. 2016, No. 5, pp. 1447-1466.
  6. Min-max minimal hypersurface in $(M^{n+1}, g)$ with $Ric_{g}>0$ and $2\leq n\leq 6$, J. Differential Geometry, 100 (2015) 129-160.
  7. Mass angular momentum inequality for axisymmetric vacuum data with small trace, Communication in Analysis and Geometry, 22, (2014) 519-571.
  8. Convexity of reduced energy and mass angular momentum inequalities (with R. Schoen), Ann. Henri Poincar\'e, 14 (2013), 1747-1773.
  9. On the existence of min-max minimal surfaces of genus g≥ 2, Commun. Contemp. Math., 19, 1750041 (2017).
  10. On the existence of min-max minimal torus, J. Geom. Anal. 20 (2010), 1026-1055.

Other writings:

Slides and videos:

Conference:

Past Teaching: