Interests

Differential Geometry, Geometric Analysis; particularly minimal surfaces and mean curvature flow.

Publications and preprints

  1. A stable self-shrinking Möbius bundle in R4. (with K. Braxton and T.-K. Lee) Preprint.
  2. Uniqueness of free boundary minimal annuli. (with D. Parise) Preprint.
  3. A Bernstein-type theorem for capillary graphs in a half-space. (with N. Edelen and C. Li) Preprint.
  4. Free boundary and capillary minimal surfaces in spherical caps II: Low energy. Preprint.
  5. Free boundary and capillary minimal surfaces in spherical caps I: Low genus. (with K. Naff) Preprint.
  6. Half-space intersection properties for minimal hypersurfaces. (with K. Naff) J. Geom. Anal.. 35 (2025), no. 2. Published version.
  7. Uniqueness of blowups for forced mean curvature flow. (with S. Hirsch) Intl. Math. Res. Not. IMRN (2025). Published version.
  8. Sharp distance comparison for curve shortening flow on the round sphere. (with P. Bryan and M. Langford) to appear in Ann. Sc. norm. super. Pisa - Cl. sci..
  9. A distance comparison principle for curve shortening flow with free boundary. (with M. Langford) to appear in Amer. J. Math..
  10. Moving monotonicity formulae for minimal submanifolds in constant curvature. (with K. Naff) to appear in Ann. Sc. norm. super. Pisa - Cl. sci..
  11. The prescribed point area estimate for minimal submanifolds in constant curvature. (with K. Naff) to appear in Amer. J. Math..
  12. Widths of balls and free boundary minimal submanifolds. Adv. Nonlinear Stud. 23 (2023) Published version.
  13. Min-max theory for capillary surfaces. (with C. Li and X. Zhou) J. Reine Angew. Math. 2025, no. 181, 215-262. Published version.
  14. Rigidity for spherical product Ricci solitons. (with A. Sun) Comm. Anal. Geom. 33 (2025), no. 7, 1661-1706. Published version.
  15. On certain quantifications of Gromov's non-squeezing theorem. (with K. Sackel, A. Song and U. Varolgunes) Geom. Topol.. 28 (2024), no. 3, 1113-1152. Published version.
  16. Łojasiewicz inequalities for mean convex self-shrinkers. Int. Math. Res. Not. IMRN. 2023, no. 2, 1236-1254. Published version.
  17. Łojasiewicz inequalities, uniqueness and rigidity for cylindrical self-shrinkers. Camb. J. Math. 13 (2025), no. 1, 173-224. Published version.
  18. Rigidity and Łojasiewicz inequalities for Clifford self-shrinkers. (with A. Sun) Calc. Var. 64 (2025), no. 163. Published version. Associated code: clifford-public.mw
  19. Mean convex mean curvature flow with free boundary. (with N. Edelen, R. Haslhofer and M. Ivaki) Comm. Pure Appl. Math 75 (2021), no. 4, 767-817. Published version.
  20. Reilly's type inequality for the Laplacian associated to a density related with shrinkers for MCF. (with M. Carmen Domingo-Juan and V. Miquel) J. Differential Equations. 272 (2021), 958-978. Published version.
  21. Min-max theory for networks of constant geodesic curvature. (with Xin Zhou) Adv. Math.. 361 (2020), art. 106941. Published version.
  22. Existence of hypersurfaces with prescribed mean curvature I - Generic min-max. (with Xin Zhou) Camb. J. Math. 8 (2020), no. 2, 331-362. Published version.
  23. Min-max theory for constant mean curvature hypersurfaces. (with Xin Zhou) Invent. Math. 218 (2019), no. 2, 441-490. Published version.
  24. Moving-centre monotonicity formulae for minimal submanifolds and related equations. J. Funct. Anal., 274 (2018), no. 5, 1530-1552. Published version.
  25. First stability eigenvalue of singular minimal hypersurfaces in spheres. Calc. Var. Partial Differential Equations, 57 (2018), no. 5, art. 130. Published version.
  26. On the entropy of closed hypersurfaces and singular self-shrinkers. J. Differential Geom. 114 (2020), no. 3, 551-593. Published version.
  27. On the rigidity of mean convex self-shrinkers. (with Qiang Guang) Int. Math. Res. Not. IMRN, 2018, no. 20, 6406-6425. Published version.
  28. Rigidity and Curvature Estimates for Graphical Self-shrinkers. (with Qiang Guang) Calc. Var. Partial Differential Equations, 56 (2017), no. 20, art. 176. Published version.
  29. Minimal hypersurfaces with small first eigenvalue in manifolds of positive Ricci curvature, J. Topol. Anal., 9 (2017), no.3, 505-532. Published version.

A list of my papers may be additionally found on the arXiv.