Qiang Guang


Department of Mathematics

University of California, Santa Barbara

Santa Barbara, CA 93106-3080

Office: South Hall, Room 6723

Email: guang@math.ucsb.edu

I am a visiting assistant professor in the math department at UCSB. I completed my Ph.D. at MIT under the supervision of William P. Minicozzi II.

Current Teaching: Fall 2017: Math 108A, Introduction to Linear Algebra

Office Hours: Monday 2-4pm, Wednesday 2-3pm in South Hall 6723

Research Interests:

Publications and Preprints:

  1. Curvature estimates and compactness for improper minimal hypersurfaces, joint with Xin Zhou, preprint.
  2. Curvature estimates for stable free boundary minimal hypersurfaces, joint with Martin Li and Xin Zhou. https://arxiv.org/abs/1611.02605
  3. On the rigidity of mean convex self-shrinkers, joint with Jonathan J. Zhu. http://arxiv.org/abs/1603.09435. To appear in Int. Math. Res. Not.
  4. Rigidity and curvature estimates for graphical self-shrinkers, joint with Jonathan J. Zhu. Calc. Var. Partial Differential Equations 56 (2017), no. 6, 56:176.
  5. Volume growth, entropy and stability for translating solitons. https://arxiv.org/abs/1612.05312. To appear in Comm. Anal. Geom.
  6. Gap and rigidity theorems of $\lambda$-hypersurfaces. http://arxiv.org/abs/1405.4871
  7. Self-shrinkers with second fundamental form of constant length. Bull. Aust. Math. Soc. 96 (2017), no. 2, 326--332.
  8. Self-shrinkers and translating solitons of mean curvature flow, PhD thesis, Massachusetts Institute of Technology, 2016.

Expository writings/Notes:

  1. Recent progress on compactness of minimal surfaces with free boundary, joint with Xin Zhou. To appear in Proceeding of the Workshop on Geometric Analysis 2017.

Teaching and Grading: