20 citations · 43 across the 17 of their papers we have counts for
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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…
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…
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…
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…
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…
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 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…