Welcome to Qi Ding(丁琪)’s Homepage

Present Address: Shanghai Center for Mathematical Sciences, Fudan University Jiangwan Campus, 2005 Songhu Rd., Shanghai 200438, China
(上海数学中心，复旦大学江湾校区，淞沪路2005号，上海，200438，中国)

Office Phone: (+86) 021 3124 3845

Email: dingqi@fudan.edu.cn

Research interests

General research areas: Differential geometry, Geometric analysis, Partial differential equations, Geometric measure theory, Complex geometry.
Some specific topics: minimal submanifolds in Euclidean space, minimal hypersurfaces in manifolds, mean curvature flows and their self-similar solutions, Lagrangian submanifolds, elliptic equations of mean curvature type, inverse mean curvature flows

Publications

Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation, (with J.Jost and Y.L.Xin), to appear in Math. Ann., (arXiv:2109.09383)
Existence and non-existence of minimal graphs, (with J.Jost and Y.L.Xin), J. Math. Pure Appl. 179, 2023, 391-424. (arXiv:1701.01674)
Area-minimizing hypersurfaces in manifolds of Ricci curvature bounded below, J. Reine. Angew. Math. 798, 2023, 193-236. (arXiv:2107.11074)
Liouville type theorems and Hessian estimates for special Lagrangian equations, Math. Ann. 386, 2023, 1163-1200. (arXiv:1912.00604)
Boundary regularity for minimal graphs of higher codimensions, (with Y.L.Xin), Chin. Ann. Math. 43B(5), 2022, 869-876.
Minimal hypersurfaces in manifolds of Ricci curvature bounded below, J. Reine. Angew. Math. 791, 2022, 247–282. (arXiv:2109.02483)
Liouville-type theorems for minimal graphs over manifolds, Analysis & PDE 14(6), 2021, 1925-1949.(arxiv:1911.10306)
A Bernstein type theorem for minimal hypersurfaces via Gauss maps, J. Funct. Anal. 278(11), 2020, 108469.(arxiv:1803.07132)
Minimal cones and self-expanding solutions for mean curvature flows, Math. Ann. 376(1-2), 2020, 359-405.(arxiv:1503.02612)
A rigidity theorem on the second fundamental form for self-shrinkers, Trans. A.M.S. 370(12), 2018, 8311-8329.(arxiv:1701.07945)
The rigidity theorems of self shrinkers via Gauss maps, (with Y.L.Xin and Ling Yang), Adv. Math. 303(5), 2016, 151-174.(arxiv:1203.1096)
Subsequent singularities of mean convex mean curvature flows in smooth manifolds, Calc. Var. Partial Differential Equations, 55(1), 2016, 1-12.(arxiv:1502.02430)
Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature, (with J.Jost and Y.L.Xin), Amer. J. Math., 138 (2016), no.2., 287-327.(arxiv:1308.4963)
Minimal graphic functions on manifolds of non-negative Ricci curvature, (with J.Jost and Y.L.Xin), Comm. Pure Appl. Math. 69(2) (2016), 323-371.(arxiv:1310.2048)
The rigidity theorems for Lagrangian self shrinkers, (with Y.L.Xin), J. Reine. Angew. Math. 692 (2014), 109-123.(arxiv:1112.2453)
The rigidity theorems of self shrinkers, (with Y.L.Xin), Trans. A.M.S. 366 (2014), 5067-5085.(arxiv:1105.4962)
Entire spacelike translating solitons in Minkowski space, J. Funct. Anal. 265 (2013), 3133-3162.(arxiv:1204.1826)
Volume growth, eigenvalue and compactness for self-shrinkers, (with Y.L.Xin), Asian J. Math. 17 (2013), 443-456.(arxiv:1101.1411 )
On Chern’s problem for rigidity of minimal hypersurfaces in the spheres, (with Y.L.Xin), Adv. Math. 227(2011), 131-145.(arxiv:1012.1073)
The inverse mean curvature flow in rotationally symmetric spaces, Chin. Ann. Math. 32B(1), 2011, 27-44.

Preprints

Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature, arXiv:2401.03394.
Capacity for minimal graphs over manifolds and the half-space property, arXiv:2306.15137.
Poincare inequality on minimal graphs over manifolds and applications, arXiv:2111.04458.
Boundary regularity for mean curvature flows of higher codimension, (with J.Jost and Y.L.Xin), arXiv:1706.01412.
On the self-shrinking systems in arbitrary codimensional spaces, (with Zhizhang Wang), arXiv:1012.0429, 2010.

Education

Fudan University, Shanghai, China
Ph.D in Mathematics, June, 2012
Thesis Advisor: Prof. Yuanlong Xin
Thesis Topic: Some problems on geometric evolution equations
Southeast University, Nanjing, China
B.S. in Mathematics, June, 2007

Employment

Associate Professor, Shanghai Center for Mathematical Sciences, Fudan university, from July 2020
Visiting Scholar, Massachusetts Institute of Technology, U.S., Nov. 2017-Oct. 2018
Assistant Professor, Shanghai Center for Mathematical Sciences, Fudan university, July 2016-June 2020
Young Investigator, Shanghai Center for Mathematical Sciences, Fudan university, Sep. 2014-June 2016
Postdoctoral Fellow, Max Planck Institute for Mathematics in the Sciences(Leipzig), July 2012-Aug. 2014