Qiang Guang

Research Interests

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

Publications and Preprints

• The L_p-Minkowski problem with super-critical exponents,  joint with Qi-Rui Li and Xu-Jia Wang, J. Eur. Math. Soc. (JEMS), to appear, arXiv:2203.05099.

• Existence of hypersurfaces with prescribed centroaffine curvature,  joint with Qi-Rui Li and Xu-Jia Wang,  Trans. Amer. Math. Soc. 377(2024), no. 2, 841–862.

•  Flow by Gauss curvature to the L_p dual Minkowski problem, joint with Qi-Rui Li and Xu-Jia Wang, Math. Eng. 5 (2023), no. 3, Paper No. 049, 19 pp.

• The Minkowski problem in the sphere, joint with Qi-Rui Li and Xu-Jia Wang,  J. Differential Geom. 128 (2) 723 - 771, October 2024.

• A note on mean convex λ-surfaces in R^3. Proc. Amer. Math. Soc. 149 (2021), no. 3, 1259–1266.

• Min-max theory for free boundary minimal hypersurfaces II--General Morse index bounds and applications, joint with Martin Li, Zhichao Wang and Xin Zhou. Math. Ann. 379 (2021), no. 3-4, 1395–1424.

• Compactness and generic finiteness for free boundary minimal hypersurfaces (I), joint with Zhichao Wang and Xin Zhou. Pacific J. Math. 310 (2021), no. 1, 85–114.

• Free boundary minimal hypersurfaces with least area, joint with Zhichao Wang and Xin Zhou. Comm. Anal. Geom.31(2023), no.5, 1177–1215.

• 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.

• Volume growth, entropy and stability for translating solitons. Comm. Anal. Geom. 27 (2019), no. 1, 47-72.

• Rigidity and curvature estimates for graphical self-shrinkers, joint with Jonathan J. Zhu. Calc. Var. Partial Differential Equations 56 (2017), no. 6, 56:176.

• Gap and rigidity theorems of λ-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.

Links

MSI at ANU,  UCSB Math,  MIT Math, JHU Math, Zhejiang Univ Math