Lu Wang

About Me

I am a Professor in the Department of Mathematics at Yale University. My research interests lie in geometric analysis and differential geometry, with a particular focus on geometric flows – such as mean curvature flow and Ricci flow – and minimal surfaces.

I previously held faculty positions at Caltech and UW–Madison. I received my Ph.D. in Mathematics from MIT in 2011, under the supervision of Tobias H. Colding. I completed my postdoctoral training at MSRI (now SLMath), Johns Hopkins, and Imperial College London.

News

• Teaching Math 5260 (Introduction to Differentiable Manifolds) in Fall 2025
• Co-organizing the Geometric Analysis Seminar

Publications

My research is partially supported by the NSF.

Original Research Articles by Topics

Expanders of Mean Curvature Flow

• Existence of monotone Morse flow lines of the expander functional (with J. Bernstein and L. Chen), to appear in Trans. Amer. Math. Soc. arXiv: 2404.08541
• An integer degree for asymptotically conical self-expanders (with J. Bernstein), Calc. Var. Partial Differential Equations 62 (2023), no. 7, Paper No. 200, 46 pp arXiv: 1807.06494
• Topological uniqueness for self-expanders of small entropy (with J. Bernstein), Camb. J. Math. 10 (2022), no. 4, 785–833 arXiv: 1902.02642
• A mountain-pass theorem for asymptotically conical self-expanders (with J. Bernstein), Peking Math. J. 5 (2022), no. 2, 213–278 arXiv: 2003.13857
• Relative expander entropy in the presence of a two-sided obstacle and applications (with J. Bernstein), Adv. Math. 399 (2022), Paper No. 108284, 48 pp arXiv: 1906.07863
• Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow (with J. Bernstein), Int. Math. Res. Not. IMRN 2021, no. 12, 9016–9044 arXiv: 1804.09076
• The space of asymptotically conical self-expanders of mean curvature flow (with J. Bernstein), Math. Ann. 380 (2021), no. 1-2, 175–230 arXiv: 1712.04366

Hypersurfaces of Low Entropy

• Lower bounds on density for topologically nontrivial minimal cones up to dimension six (with J. Bernstein), Forum Math. Sigma 13 (2025), Paper No. e122, 18 pp arXiv: 2404.04382
• Closed hypersurfaces of low entropy in R⁴ are isotopically trivial (with J. Bernstein), Duke Math. J. 171 (2022), no. 7, 1531–1558 arXiv: 2003.13858
• Hausdorff stability of the round two-sphere under small perturbations of the entropy (with J. Bernstein), Math. Res. Lett. 25 (2018), no. 2, 347–365 arXiv: 1608.02314
• Topology of closed hypersurfaces of small entropy (with J. Bernstein), Geom. Topol. 22 (2018), no. 2, 1109–1141 arXiv: 1511.00387
• A sharp lower bound for the entropy of closed hypersurfaces up to dimension six (with J. Bernstein), Invent. Math. 206 (2016), no. 3, 601–627 arXiv: 1406.2966

Shrinkers of Mean Curvature Flow

• Asymptotic structure of self-shrinkers arXiv: 1610.04904
• A topological property of asymptotically conical self-shrinkers of small entropy (with J. Bernstein), Duke Math. J. 166 (2017), no. 3, 403–435 arXiv: 1504.01996
• Uniqueness of self-similar shrinkers with asymptotically cylindrical ends, J. Reine Angew. Math. 715 (2016), 207–230 DOI
• A remark on a uniqueness property of high multiplicity tangent flows in dimension 3 (with J. Bernstein), Int. Math. Res. Not. IMRN 2015, no. 15, 6286–6294 arXiv: 1402.6687
• Uniqueness of self-similar shrinkers with asymptotically conical ends, J. Amer. Math. Soc. 27 (2014), no. 3, 613–638 arXiv: 1110.0450
• A Bernstein type theorem for self-similar shrinkers, Geom. Dedicata 151 (2011), 297–303 arXiv: 0912.1809

Shrinking Ricci Solitons

• Isometries of asymptotically conical shrinking Ricci solitons (with B. Kotschwar), Comm. Anal. Geom. 32 (2024), no. 1, 1–19 arXiv: 1901.00044
• A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons (with B. Kotschwar), J. Differential Geom. 126 (2024), no. 1, 215–295 arXiv: 1712.03185
• Rigidity of asymptotically conical shrinking gradient Ricci solitons (with B. Kotschwar), J. Differential Geom. 100 (2015), no. 1, 55–108 arXiv: 1307.4746

Harmonic Map Heat Flow

• Harmonic map heat flow with rough boundary data, Trans. Amer. Math. Soc. 364 (2012), no. 10, 5265–5283 arXiv: 1010.3313
• Existence of good sweepouts on closed manifolds (with L. Lin), Proc. Amer. Math. Soc. 138 (2010), no. 11, 4081–4088 arXiv: 0907.2724

Polynomial Differential Systems

• A quartic system and a quintic system with fine focus of order 18 (with J. Huang, F. Wang, and J. Yang), Bull. Sci. Math. 132 (2008), no. 3, 205–217 DOI

Expository Articles

• Colding-Minicozzi entropy and complexity of submanifolds (with J. Bernstein), Notices Amer. Math. Soc. 71 (2024), no. 7, 861–867 DOI
• Entropy in mean curvature flow, ICM–International Congress of Mathematicians, Vol. 4, Sections 5–8, 2656–2676, EMS Press, Berlin, 2023 DOI

Theses

• Self-shrinkers of mean curvature flow and harmonic map heat flow with rough boundary data, Thesis (Ph.D.)–Massachusetts Institute of Technology, ProQuest LLC, Ann Arbor, MI, 2011 URI