4 citations · 7 across the 8 of their papers we have counts for
9 papers
On the geometry and uniqueness of asymptotically locally hyperbolic static vacuum black holes
Brian Harvie, Ye-Kai Wang
We establish several geometric characterizations and rigidity results for 3-dimensional asymptotically locally hyperbolic (ALH) static spaces with horizon boundary. Notably, a 3-di…
A Penrose-type inequality for static spacetimes
Brian Harvie
We establish a lower bound on the total mass of the time slices of (n + 1)-dimensional asymptotically flat standard static spacetimes under the timelike convergence condition. The…
On weak inverse mean curvature flow and Minkowski-type inequalities in hyperbolic space
Brian Harvie
We prove that a proper weak solution to inverse mean curvature flow in , , is smooth and star-shaped by the time \…
Quasi-spherical metrics and the static Minkowski inequality
Brian Harvie, Ye-Kai Wang
We prove that equality within the Minkowski inequality for asymptotically flat static manifolds is achieved only by slices of Schwarzschild space.
A rigidity theorem for asymptotically flat static manifolds and its applications
Brian Harvie, Ye-Kai Wang
In this paper, we study the Minkowski-type inequality for asymptotically flat static manifolds with boundary and with dimension that was establishedby McCormi…
The mass of the static extension of small spheres
Brian Harvie, Ye-Kai Wang
We give a simple proof to the computation of ADM mass of the static extensions of small spheres in Wiygul \cite{W1, W2}. It makes use of the mass formula $m = \frac{1}{4π} \int_{\p…
The Limit of the Inverse Mean Curvature Flow on a Torus
Brian Harvie
For an rotationally symmetric embedded torus , evolved by Inverse Mean Curvature Flow, we show that the total curvature remains bounded up…
Inverse Mean Curvature Flow of Rotationally Symmetric Hypersurfaces
Brian Harvie
We prove that the Inverse Mean Curvature Flow of a non-star-shaped, mean-convex embedded sphere in with symmetry about an axis and sufficiently long, thick necks…
Inverse Mean Curvature Flow over Non-Star-Shaped Surfaces
Brian Harvie
We derive an upper bound on the waiting time for a variational weak solution to Inverse Mean Curvature Flow in to become star-shaped. As a consequence, we demons…