Qiang Guang
Email: qguang8@gmail.com
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, 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, preprint, to appear in J. Differential Geom., 2020.
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. arXiv:1801.07036. To appear in Comm. Anal. Geom.
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.