Publications

Journal Publications

  1. 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.
  2. Topology of closed hypersurfaces of small entropy (with J. Bernstein). Geom. Topol. 22 (2018), no. 2, 1109-1141.
  3. A topological property of asymptotically conical self-shrinkers of small entropy (with J. Bernstein). Duke Math. J. 166 (2017), no. 3, 403-435.
  4. 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.
  5. Uniqueness of self-similar shrinkers with asymptotically cylindrical ends. J. Reine Angew. Math. 715 (2016), 207-230.
  6. 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.
  7. Rigidity of asymptotically conical shrinking gradient Ricci solitons (with B. Kotschwar). J. Differential Geom. 100 (2015), no. 1, 55-108.
  8. Uniqueness of self-similar shrinkers with asymptotically conical ends. J. Amer. Math. Soc. 27 (2014), no. 3, 613-638.
  9. Harmonic map heat flow with rough boundary data. Trans. Amer. Math. Soc. 364 (2012), no. 10, 5265-5283.
  10. A Bernstein type theorem for self-similar shrinkers. Geom. Dedicata 151 (2011), 297-303.
  11. Existence of good sweepouts on closed manifolds (with L. Lin). Proc. Amer. Math. Soc. 138 (2010), 4081-4088.
  12. 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

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

Conference Reports, Lecture Notes, etc.

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