• Research interests
  
  
  • Geometric Analysis, Differential Geometry, Nonlinear Partial Differential Equations.



• Publications and Preprints
  
  
  • Asymptotic behavior of unstable perturbations of the Fubini-Study metric in Ricci flow
    Submitted. (Joint with D. Garfinkle, D. Knopf, and J. Isenberg)
  • The modified Kähler-Ricci flow, II.
    Submitted. (Joint with Z. Zhang)
  • The second Robin eigenvalue in non-compact rank-1 symmetric spaces
    Submitted. (Joint with X. Li and K. Wang)
  • An upper bound for the first nonzero Steklov eigenvalue
    Submitted. (Joint with X. Li and K. Wang)
  • Asymptotic analysis of Ricci flow on Rⁿ⁺¹ with Type-IIb singularities
    Submitted.
  • A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with type-II curvature blowup: II
    Experimental Mathematics (2023), DOI: https://doi.org/10.1080/10586458.2023.2201958 (Joint with D. Garfinkle, D. Knopf, and J. Isenberg)
  • On the second Robin eigenvalue of the Laplacian
    Calculus of Variations and Partial Differential Equations, 62 (2023), no.9, Paper No. 256, 17 pp. . (Joint with X. Li and K. Wang)
  • A quantitative Bucur-Henrot inequality
    Mathematische Nachrichten, 295 (2022), 2436–2451. (Joint with K. Wang)
  • On the precise asymptotics of Type-IIb solutions to mean curvature flow
    Transactions of the American Mathematical Society. Series B, 9 (2022), 564–585. (Joint with J. Isenberg and Z. Zhang)
  • A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with type-II curvature blowup
    Nonlinearity 34 (2021) 6539–6560. (Joint with D. Garfinkle, D. Knopf, and J. Isenberg)
  • Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up. II
    Advances in Mathematics 367 (2020), 107111. (Joint with J. Isenberg and Z. Zhang)
  • Type-II singularities in mean curvature flow
    Surveys in Geometric Analysis 2019, to appear (Joint with Z. Zhang)
  • Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up
    Journal für die reine und angewandte Mathematik (Crelle) 754 (2019), 225–251. (Joint with J. Isenberg)
  • Metrics with non-negative Ricci curvature on convex three-manifolds
    Geometry & Topology 20 (2016), no.5, 2905–2922. (Joint with A. Aché and D. Maximo)
  • Dynamical stability of algebraic Ricci solitons
    Journal für die reine und angewandte Mathematik (Crelle) 713 (2016), 225–243. (Joint with M. B. Williams)
  • On type-II singularities in Ricci flow on R^N
    Communications in Partial Differential Equations 39 (2014), no. 11, 2064–2090.
  • Stability of complex hyperbolic space under curvature-normalized Ricci flow
    Geometriae Dedicata 164 (2013), 231–258.
  • On isoperimetric surfaces in general relativity. II
    Journal of Geometry and Physics 59 (2009), no. 11, 1453–1460. (Joint with F. Abedin, J. Corvino, and S. Kapita)
  • On the center of mass of isolated systems
    Classical and Quantum Gravity 25 (2008), no. 8, 085008, 18 pp. (Joint with J. Corvino)