RESEARCH
1. Monotonicity of the p-Green functions (with P.-Y. Chan, J. Chu and M.-C. Lee)
-Established a general monotonicity formula of p-Green functions
-Characterised Euclidean space among NNSC 3-manifolds
-https://arxiv.org/abs/2202.13832 (submitted)
2. On a spacetime positive mass theorem with corners
-Showed the ADM mass lower bound in terms of the jump on mean curvature and conjugate momentum
-Found a new notion of quasilocal mass which detects minimal surfaces on initial data sets
-Discovered sufficient conditions for the non-existence of DEC fill-ins
-https://arxiv.org/abs/2109.11070 (submitted)
3. Dihedral rigidity of cubic initial data sets
-Provided a new perspective on and proved Gromov’s dihedral rigidity theorem
-Showed a new path for showing existence of marginally trapped surfaces
-Provided a new proof of the spacetime positive mass theorem
-https://arxiv.org/abs/2108.08942 (submitted)
4. Mass of asymptotically flat 3-manifolds with boundary (with S. Hirsch and P. Miao)
-Discussed lower bound of ADM mass on manifolds with boundary
-Proved convergence of the Brown York mass to the ADM mass on a general family of surfaces
-https://arxiv.org/abs/2009.02959, Accepted by Communications in Analysis and Geometry
