# Publications

**Journal Publications**

*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.*Topology of closed hypersurfaces of small entropy*(with J. Bernstein).*A topological property of asymptotically conical self-shrinkers of small entropy*(with J. Bernstein). Duke Math. J. 166 (2017), no. 3, 403-435.*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.*Uniqueness of self-similar shrinkers with asymptotically cylindrical ends*. J. Reine Angew. Math. 715 (2016), 207-230.*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.*Rigidity of asymptotically conical shrinking gradient Ricci solitons*(with B. Kotschwar). J. Differential Geom. 100 (2015), no. 1, 55-108.*Uniqueness of self-similar shrinkers with asymptotically conical ends*. J. Amer. Math. Soc. 27 (2014), no. 3, 613-638.*Harmonic map heat flow with rough boundary data*. Trans. Amer. Math. Soc. 364 (2012), no. 10, 5265-5283.*A Bernstein type theorem for self-similar shrinkers*. Geom. Dedicata 151 (2011), 297-303.*Existence of good sweepouts on closed manifolds*(with L. Lin). Proc. Amer. Math. Soc. 138 (2010), 4081-4088.*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.

**Preprints**

*Asymptotic structure of self-shrinkers*. Preprint. ArXiv.*A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons*(With B. Kotschwar)*.*Preprint. ArXiv.*The space of asymptotically conical self-expanders of mean curvature flow*(With J. Bernstein). Preprint. ArXiv.*Smooth compactness for spaces of asymptotically conical self-expanders of mean curvature flow*(With J. Bernstein). Preprint. ArXiv.*An integer degree for asymptotically conical self-expanders*(With J. Bernstein). Preprint. Arxiv.

**Conference Reports, Lecture Notes, etc.**

*The space of asymptotically conical self-expanders of mean curvature flow,*Oberwolfach Reports, 2018.*Mean curvature flow and entropy*(extended abstract), Oberwolfach Reports, 2017.*Asymptotic structure of self-shrinkers of mean curvature flow*(extended abstract), Oberwolfach Reports, 2017.