50 citations · 70 across the 8 of their papers we have counts for
10 papers
Sobolev-class asymptotically hyperbolic manifolds and the Yamabe problem
Paul T. Allen, John M. Lee, David Maxwell
We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class regularity, and introduce several technical tools for studying PDEs on such manifolds. Our results…
Asymptotic gluing of shear-free hyperboloidal initial data sets
Paul T. Allen, James Isenberg, John M. Lee +1
We present a procedure for asymptotic gluing of hyperboloidal initial data sets that preserves the shear-free condition. Our construction is modeled on a previous gluing constructi…
The shear-free condition and constant-mean-curvature hyperboloidal initial data
Paul T. Allen, James Isenberg, John M. Lee +1
We consider the Einstein-Maxwell-fluid constraint equations, and make use of the conformal method to construct and parametrize constant-mean-curvature hyperboloidal initial data se…
Smoothly compactifiable shear-free hyperboloidal data is dense in the physical topology
Paul T. Allen, Iva Stavrov Allen
We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in…
Weakly asymptotically hyperbolic manifolds
Paul T. Allen, James Isenberg, John M. Lee +1
We introduce a class of "weakly asymptotically hyperbolic" geometries whose sectional curvatures tend to and are , but are not necessarily , conformally compact. We…
The Dirichlet problem for curve shortening flow
Paul T. Allen, Adam Layne, Katharine Tsukahara
We investigate the evolution of open curves with fixed endpoints under the curve shortening flow, which evolves curves in proportion to their curvature. Using a distance comparison…