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.

Current Teaching: I am not teaching in Winter 2019

Office Hours: By appointment in South Hall 6501

Research Interests:

• Geometric analysis and Geometric PDEs, Mean curvature flow, Minimal surfaces.

Publications and Preprints:

1. Compactness and generic finiteness for free boundary minimal hypersurfaces, joint with Zhichao Wang and 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. Int. Math. Res. Not. IMRN 2018, no. 20, 6406-6425.
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