I got my PhD at UC Irvine under Prof. Richard Schoen's supervision. Before that, I obtained my MPhil under Prof. Luen-Fai Tam's guidance. My research interests include differential geometry and partial differential equations. My works are mainly on scalar curvature and general relativity, including the energy and the shape of initial data sets from both local and global perspectives.
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Email: tytsang [at] uci [dot] edu
RESEARCH
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
TEACHING
NYU (Instructor):
Mathematics for Economcis I (MATH016)
Linear Algebra I (MATH140)
UC Irvine (Teaching Assistant):
Single variable calculus (MATH2A)
Multivariable calculus (MATH2D, 2E)
The Chinese University of Hong Kong (Teaching Assistant):
Linear algebra (MATH1030)
Elementary analysis (MATH2050, 2060)
Metric space topology and analysis (MATH3060)
Measure theory (MATH4050)
Last updated: 24th Apr, 2024.
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