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

Geometry and Analysis on Manifolds 2017.

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:

Grant:

Preprints:

  1. Min-max theory for free boundary minimal hypersurfaces I - regularity theory (joint with Martin Li), arXiv:1611.02612.
  2. Curvature estimates for stable free boundary minimal hypersurfaces (joint 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 (joint with Y. Liokumovich), International Mathematics Research Notices. arXiv:1510.02896v1.
  2. Entropy of closed surfaces and min-max theory (joint with D. Ketover), accepted by J. Differential Geometry, arXiv:1509.06238.
  3. Existence of minimal surfaces of arbitrary large Morse index (joint 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 Volume 105, Number 2 (2017), 291-343., arXiv:1504.00966.
  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 (jointed with R. Schoen), Ann. Henri Poincar\'e, 14 (2013), 1747-1773.
  9. On the existence of min-max minimal surfaces of genus g≥ 2, accepted by Communications in Contemporary Mathematics, arXiv:1111.6206.
  10. On the existence of min-max minimal torus, J. Geom. Anal. 20 (2010), 1026-1055.

Other writings:

Slides and videos:

Past Teaching: