20 citations · 43 across the 17 of their papers we have counts for
20 papers
A metric on with positive sectional curvature
S. Brendle, P. K. Hung
We construct a metric on with positive sectional curvature. Starting from the standard metric on , we first perform a Cheeger deformation. The resu…
The rigidity statement in the Horowitz-Myers conjecture
S. Brendle, P. K. Hung
In this paper, we give an alternative proof of the Horowitz-Myers conjecture in dimension . Moreover, we show that a metric that achieves equality in the Horowitz-…
Systolic inequalities and the Horowitz-Myers conjecture
S. Brendle, P. K. Hung
Let be an integer with , let be a compact manifold of dimension with boundary , and let be a Riemannian metric on with scalar curva…
Thom's gradient conjecture for nonlinear evolution equations
Beomjun Choi, Pei-Ken Hung
R. Thom's gradient conjecture states that if a gradient flow of an analytic function converges to a limit, it does so along a unique limiting direction. In this paper, we extend an…
Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori
Aghil Alaee, Pei-Ken Hung, Marcus Khuri
A classic result of Shi and Tam states that a 2-sphere of positive Gauss and mean curvature bounding a compact 3-manifold with nonnegative scalar curvature, must have total mean cu…
Asymptotics for slowly converging evolution equations
Beomjun Choi, Pei-Ken Hung
We investigate slowly converging solutions for non-linear evolution equations of elliptic or parabolic type. These equations arise from the study of isolated singularities in geome…
The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
Aghil Alaee, Pei-Ken Hung, Marcus Khuri
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped bound…
A Minkowski-type inequality in the AdS-Melvin space
Daniel Xia, Pei-Ken Hung
The AdS-Melvin spacetime was introduced by Astorino and models the AdS soliton with electromagnetic charge. It is a static spacetime with a time-symmetric Cauchy hypersurface, whic…
Determinantal structures for Bessel fields
Lucas Benigni, Pei-Ken Hung, Xuan Wu
A Bessel field is a two-variable random field such that for every , has the law of a…
A Minkowski inequality for Horowitz-Myers geon
Aghil Alaee, Pei-Ken Hung
We prove a sharp inequality for toroidal hypersurfaces in three and four dimensional Horowitz-Myers geon. This extend previous results on Minkowski inequality in the static spaceti…
The linear stability of the Schwarzschild spacetime in the harmonic gauge: even part
Pei-Ken Hung
In this paper we study the even part of the linear stability of the Schwarzschild spacetime as a continuation of [22]. By taking the harmonic gauge, we prove that the energy decays…
Inverse Mean Curvature Flow with Singularities
Beomjun Choi, Pei-Ken Hung
This paper concerns the inverse mean curvature flow of convex hypersurfaces which are Lipschitz in general. After defining a weak solution, we study the evolution of the singularit…
Linear Stability of Higher Dimensional Schwarzschild Spacetimes: Decay of Master Quantities
Pei-Ken Hung, Jordan Keller, Mu-Tao Wang
In this paper, we study solutions to the linearized vacuum Einstein equations centered at higher-dimensional Schwarzschild met- rics. We employ Hodge decomposition to split solutio…
The linear stability of the Schwarzschild spacetime in the harmonic gauge: odd part
Pei-Ken Hung
In this paper, we study the odd solution of the linearlized Einstein equation on the Schwarzschild background and in the harmonic gauge. With the aid of Regge-Wheeler quantities, w…
Linear Stability of Schwarzschild Spacetime: Decay of Metric Coefficients
Pei-Ken Hung, Jordan Keller, Mu-Tao Wang
In this paper, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, w…
Linear stability of Schwarzschild spacetime subject to axial perturbations
Pei-Ken Hung, Jordan Keller
In this paper, we address the issue of linear stability of Schwarzschild space- time subject to certain axisymmetric perturbations. In particular, we prove that associ- ated soluti…
Area bounds for minimal surfaces that pass through a prescribed point in a ball
S. Brendle, P. K. Hung
Let be a -dimensional minimal submanifold in the -dimensional unit ball which passes through a point and satisfies . We…
A sharp inscribed radius estimate for fully nonlinear flows
Simon Brendle, Pei-Ken Hung
We prove a sharp estimate for the inscribed radius under certain fully nonlinear curvature flows. This estimate is asymptotically sharp on cylinders.
The rest mass of an asymptotically Anti-de Sitter spacetime
Po-Ning Chen, Pei-Ken Hung, Mu-Tao Wang +1
We study the space of Killing fields on the four dimensional AdS spacetime . Two subsets and are identified: (the spinor Killin…
Inverse mean curvature flows in the hyperbolic 3-space revisited
Pei-Ken Hung, Mu-Tao Wang
This note revisits the inverse mean curvature flow in the 3-dimensional hyperbolic space. In particular, we show that the limiting shape is not necessarily round after scaling, thu…