Research

I specialize in differential geometry and geometric analysis. More specifically, I am interested in geometric flows (long-time existence, regularity, monotonicity formulae), geometric inequalities for hypersurfaces (Minkowski inequalities, isoperimetric inequalities), and mathematical problems in general relativity (classifications of static and stationary spacetimes, the Penrose inequality).

• Publications and preprints

• A Penrose-Type Inequality for Static Spacetimes

Preprint. arXiv.

• Quasi-Spherical Metrics and the Static Minkowski Inequality (Joint w/ Ye-Kai Wang)

Preprint. arXiv.

•   On Weak Inverse Mean Curvature Flow and Minkowski-Type Inequalities in Hyperbolic Space

Preprint. arXiv.

• A Rigidity Theorem for Asymptotically Flat Static Manifolds and its Applications (Joint w/ Ye-Kai Wang)

Transactions of the American Mathematical Society 377 No. 5 (2024), 3599-3629. arXiv. Journal.

• The Mass of the Static Extension of Small Spheres (Joint w/ Ye-Kai Wang)

International Mathematics Research Notices, Vol. 2024, No. 2 (2024). arXiv. Journal.

• Inverse Mean Curvature Flow of Rotationally Symmetric Hypersurfaces

Calculus of Variations and Partial Differential Equations 62, No. 125 (2023). arXiv. Journal.

• The Limit of the Inverse Mean Curvature Flow on a Torus

Proceedings of the American Mathematical Society 150 (2022), 3049-3061. arXiv. Journal.

• Inverse Mean Curvature Flow over Non-Star-Shaped Surfaces

Mathematical Research Letters, Vol. 29, No. 4 (2022), 1065-1086. arXiv. Journal.

• Dissertation

• The Inverse Mean Curvature Flow: Singularities, Dynamical Stability, and Applications to Minimal Surfaces

Proquest, LLC (2021). Published Version.

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“I am so clever that sometimes I don't understand a single word of what I am saying.”

-Oscar Wilde