Research

1. The Dirichlet problem for the prescribed curvature equations in Minkowski space II.

In preparation.

2. Interior curvature estimates for hypersurfaces of prescribed curvature quotients.

Completed work. Still trying to reach for better results. Hence not intending for peer review at the moment.

3. Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II.

Preprint on arXiv. 

[arXiv link]

4. The Dirichlet problem for the prescribed curvature equations in Minkowski space. 

J. Funct. Anal. 289 (2025), no. 11, Paper No. 111149.

[arXiv link, journal link]

5. (Ph.D. thesis) Hypersurfaces of constant scalar curvature in hyperbolic space with prescribed asymptotic boundary at infinity. 

Adv. Math. 480 (2025), Paper No. 110493.

[arXiv link, journal link] 

6. Starshaped Compact Hypersurfaces in Warped Product Manifolds II: A Class of Hessian Type Equations.

J. Geom. Anal. 35 (2025), no. 1, Paper No. 24. 

[arXiv link, journal link] 

7. Starshaped Compact Hypersurfaces in Warped Product Manifolds I: Prescribed Curvature Equations.

Calc. Var. Partial Differential Equations 63 (2024), no.9, Paper No. 241.  

[arXiv link, journal link]

8. (M.Sc. thesis) Curvature Estimates for Hypersurfaces of Constant Curvature in Hyperbolic Space. 

Math. Res. Lett. 31 (2024), no. 4, 1197–1213.  

[arXiv link, journal link]