Contact

Email: pkhung@illinois.edu

Department of Mathematcis,  University of Illinois Urbana-Champaign

Office: Altgeld 308

Papers

• Determinantal structures for Bessel fields, with L. Benigni and X. Wu, to appear on Ann. Inst. Henri Poincaré. (2024+)

• Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori with A. Alaee and M. Khuri, to appear on Proc. Amer. Math. Soc. (2024+)

• Inverse mean curvature flow with singularities with B. Choi, Int. Math. Res. Not. IMRN. (2023)

• The positive energy theorem for asymptotically hyperboloidal initial data sets with toroidal infinity and related rigidity results with A. Alaee and M. Khuri, Comm. Math. Phys. (2022).

• A Minkowski inequality for Horowitz-Myers geon, with A. Alaee, J. Geom. Anal. (2022)

• Linear stability of Schwarzschild spacetime: Decay of metric coefficients with J. Keller and M.-T. Wang, J. Differential Geom. (2020).

• Linear stability of higher dimensional Schwarzschild spacetimes: decay of master quantities with J. Keller and M.-T. Wang, Ann. PDE (2020).

• A sharp inscribed radius estimate for fully nonlinear flows with S. Brendle, Amer. J. Math. (2019).

• The Rest Mass of an Asymptotically Anti-de Sitter Spacetime with P.-N. Chen, M.-T. Wang and S.-T. Yau, Ann. Henri Poincaré. (2017).

• Area Bounds for Minimal Surfaces that Pass Through a Prescribed Point in a Ball with S. Brendle, Geom. Funct. Anal. (2017).

• A Minkowski Inequality for Hypersurfaces in the Anti-de Sitter-Schwarzschild Manifold with S. Brendle and M.-T. Wang, Comm. Pure Appl. Math. (2016).

• Inverse mean curvature flows in the hyperbolic 3-space revisited with M.-T. Wang, Calc. Var. Partial Differential Equations (2015).

preprints

• Systolic inequalities and the Horowitz-Myers conjecture, with S. Brendle, (2024)

• Thom's gradient conjecture for nonlinear evolution equations, with B. Choi, (2024)

• A Minkowski-type inequality in the AdS-Melvin space , with D. Xia, (2021).

• The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part, (2019).

• The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part, (2018).

• Linear stability of Schwarzschild spacetime subject to axial perturbations, (2020).