Qiang Guang

Address:

Department of Mathematics

University of California, Santa Barbara

Santa Barbara, CA 93106-3080

Office: South Hall, Room 6501

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.

UCSB Differential Geometry Seminar

Current Teaching: Fall 2018: Math 108B, Advanced Linear Algebra; Math 4B, Differential Equations

Office Hours: Mon&Wed 3:00-4:30pm in South Hall 6501

Research Interests:

Publications and Preprints:

  1. Compactness and generic finiteness for free boundary minimal hypersurfaces, joint with Xin Zhou. arXiv:1803.01509
  2. Free boundary minimal hypersurfaces with least area, joint with Zhichao Wang and Xin Zhou. arXiv:1801.07036
  3. Curvature estimates for stable free boundary minimal hypersurfaces, joint with Martin Li and Xin Zhou. arXiv:1611.02605. To appear in J. Reine Angew. Math.
  4. On the rigidity of mean convex self-shrinkers, joint with Jonathan J. Zhu. arXiv:1603.09435. To appear in Int. Math. Res. Not.
  5. Rigidity and curvature estimates for graphical self-shrinkers, joint with Jonathan J. Zhu. Calc. Var. Partial Differential Equations 56 (2017), no. 6, 56:176.
  6. Volume growth, entropy and stability for translating solitons. arXiv:1612.05312. To appear in Comm. Anal. Geom.
  7. Gap and rigidity theorems of $\lambda$-hypersurfaces. Proc. Amer. Math. Soc. 146 (2018), no. 10, 4459-4471.
  8. Self-shrinkers with second fundamental form of constant length. Bull. Aust. Math. Soc. 96 (2017), no. 2, 326--332.
  9. 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, Surveys in Geometric Analysis 2017, 63-78, Science Press Beijing, Beijing, 2018

Teaching and Grading:

Other: