# Qiang Guang

MSI Fellow

Employment

• 08/2019 - present, MSI fellow, Australian National University
• 07/2016 - 07/2019, Visiting Assistant Professor, University of California, Santa Barbara

Education

### Research interests

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

### Groups

• Min-max theory for free boundary minimal hypersurfaces II--General Morse index bounds and applications, joint with Martin Li, Zhichao Wang and Xin Zhou. arXiv:1907.12064. To appear in Math. Ann.
• Compactness and generic finiteness for free boundary minimal hypersurfaces (I), joint with Zhichao Wang and Xin Zhou. arXiv:1803.01509
• Free boundary minimal hypersurfaces with least area, joint with Zhichao Wang and Xin Zhou. arXiv:1801.07036
• Curvature estimates for stable free boundary minimal hypersurfaces, joint with Martin Li and Xin Zhou. J. Reine Angew. Math.759 (2020), 245–264.
• On the rigidity of mean convex self-shrinkers, joint with Jonathan J. Zhu. Int. Math. Res. Not. IMRN 2018, no. 20, 6406-6425.
• Rigidity and curvature estimates for graphical self-shrinkers, joint with Jonathan J. Zhu. Calc. Var. Partial Differential Equations 56 (2017), no. 6, 56:176.
• Volume growth, entropy and stability for translating solitons. Comm. Anal. Geom. 27 (2019), no. 1, 47-72.
• Gap and rigidity theorems of $\lambda$-hypersurfaces. Proc. Amer. Math. Soc. 146 (2018), no. 10, 4459-4471.
• Self-shrinkers with second fundamental form of constant length. Bull. Aust. Math. Soc.96 (2017), no. 2, 326--332.
• Self-shrinkers and translating solitons of mean curvature flow, PhD thesis, Massachusetts Institute of Technology, 2016.

• ### Expository writings/Notes

• 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