A tilted spacetime positive mass theorem. arXiv. See expanded version here.
Scalar curvature rigidity of domains in a 3-dimensional warped product (with Gaoming Wang). arXiv.
Scalar curvature rigidity of domains in a warped product. (with Xueyuan Wan). arXiv (This paper contains improvements over results from a previous preprint arXiv:2312.16022 about hyperbolic dihedral rigidity; a Llarull theorem is added)
Publication
A constrained mean curvature flow on capillary hypersurface supported on totally geodesic plane. (with Yimin Chen). arXiv, DOI.
Band width estimates of CMC initial data sets (with Xueyuan Wan). Accepted in CAG on 2 Feb, 2025. arXiv, see CAG notice. (This supercedes previous papers 2107.12782, 2107.12784).
Spectral constant rigidity of warped product metrics (with Juncheol Pyo, Xueyuan Wan). J. Lond. Math. Soc. (2) 110 (2024), no.1, Paper No. e12958. journal, arXiv.
Inverse mean curvature flow with a free boundary in hyperbolic space. Calc. Var. Partial Differential Equations, 63, 109 (2024). journal, arXiv.
Dihedral rigidity in hyperbolic 3-space. (with Gaoming Wang) Trans. Amer. Math. Soc., 337 (2024), 807-840. journal, arXiv. (This paper contains a previous result Mass and polyhedra in asymptotically hyperbolic manifoldsarXiv:2102.10715)
A curvature estimate for stable marginally outer trapped hypersurface with a free boundary. Int. Math. Res. Not. IMRN (2024), no. 6, 4624-4655. journal, arXiv.
The mass of an asymptotically hyperbolic end and distance estimates (with Xueyuan Wan). J. of Math. Phys.63 (2022), no. 12, Paper No. 122502. journal, arXiv.
Scalar curvature, mean curvature and harmonic maps to the circle (with Inkang Kim). Annals of Global Analysis and Geometry, 62, 201–219 (2022). journal, arXiv.
Evaluation of the mass of an asymptotically hyperbolic manifold. The Journal of Geometric Analysis, 32 (7), 1-18, (2022). journal, arXiv.
Willmore type inequality using monotonicity formulas. Pacific Journal of Mathematics, 307 (1), 53-62, (2020). journal, arXiv.
Preprints
A mixed boundary value problem for Jang’s equation and the existence of free boundary marginally outer trapped surfaces. (with Martin Li) (preprints available upon query).
Band width estimates with lower spectral curvature bound. (with Yukai Sun). arXiv
Scalar curvature rigidity of domains in a 3-dimensional warped product (with Gaoming Wang). arXiv.
Initial data set rigidity results for polyhedra. (with Xueyuan Wan). arXiv (This paper contains improvements over results from a previous preprint arXiv:2312.16022 about initial data set rigidity)
Scalar curvature rigidity of domains in a warped product. (with Xueyuan Wan). arXiv (This paper contains improvements over results from a previous preprint arXiv:2312.16022 about hyperbolic dihedral rigidity; a Llarull theorem is added)
A tilted spacetime positive mass theorem. arXiv. See an expanded version here.