RESEARCH 

1. Remarks on quasi-local mass and fill-ins 

-Provided a unified perspective and a comparison of several proposals of quasilocal mass

-Resolved the blow-up obstacle of the Kijowski-Liu-Yau mass and the Wang-Yau energy 

-Extended the quasilocal mass W and DEC fill-ins into the setting of completeness and shields 

-https://arxiv.org/abs/2404.09343 (submitted) 

2. 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 Accepted by IMRN

3. 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 W 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)

4. Dihedral rigidity of cubic initial data sets 

-Posed and proved a spacetime version of Gromov’s dihedral rigidity theorem

-Provided a new proof of the spacetime positive mass theorem

-https://arxiv.org/abs/2108.08942 (submitted)

5. 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 large family of surfaces

-https://arxiv.org/abs/2009.02959 Accepted by Communications in Analysis and Geometry

TEACHING

NYU (Instructor): 

1. Mathematics for Economcis I (MATH016) 

2. Linear Algebra I (MATH140) 

UC Irvine (Teaching Assistant): 

1. Single variable calculus (MATH2A) 

2. Multivariable calculus (MATH2D, 2E) 

The Chinese University of Hong Kong (Teaching Assistant): 

1. Linear algebra (MATH1030)

2. Elementary analysis (MATH2050, 2060) 

3. Metric space topology and analysis (MATH3060) 

4. Measure theory (MATH4050) 

Last updated: 24th Apr, 2024.