Preprints

Geometric analysis

  1. Topological Bernstein Theorems for Minimal Hypersurfaces in $\mathbb{R}^4$ confined in space
    with Alexander McWeeney.
    [pdf]

  2. On the Calabi-Yau Conjectures for Minimal Hypersurfaces in Higher Dimensions
    with Alexander McWeeney.
    [pdf]

  3. Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature
    with Michael B. Law. Calculus of Variations and Partial Differential Equations 64, Article 202 (2025).
    [pdf]

Long-time behavior of nonlinear parabolic and dispersive PDEs

  1. Continuous in time bubbling and Soliton Resolution for Non-negative Solutions of the Energy-Critical Heat Flow
    [pdf]

  2. Soliton resolution for the energy-critical nonlinear heat equation in the radial case
    To appear in Analysis & PDE.
    [pdf]

  3. Trend to Equilibrium for Flows With Random Diffusion
    with Matthew Rosenzweig and Gigliola Staffilani. International Mathematics Research Notices 2024, no. 10, 8764–8781.
    [pdf]

  4. Existence of two-solitary waves with logarithmic distance for the nonlinear Klein-Gordon equation
    Communications in Contemporary Mathematics 24, no. 1, 2050091 (2022).
    [pdf]

Optimal transport and functional inequalities

  1. Spectral Obstructions to Contracting Transport Maps on Curved Spaces
    [pdf]

  2. Entropic Selection Principle for Monge’s Optimal Transport
    with Promit Ghosal.
    [pdf]

  3. Free energy minimizers with radial densities: classification and quantitative stability
    with Lauro Silini.
    [pdf]

  4. Improvement of Wu’s logarithmic Sobolev inequality via the Poisson-Föllmer process
    with Pablo López-Rivera and Yair Shenfeld. Electronic Communications in Probability 30, Paper No. 91, 1–14 (2025).
    [pdf]

  5. Stability of Hardy Littlewood Sobolev inequality under bubbling
    Calculus of Variations and Partial Differential Equations 62, Article 223 (2023).
    [pdf]