23 citations · 50 across the 11 of their papers we have counts for
13 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…
Low regularity Poincaré-Einstein metrics
Eric Bahuaud, John M Lee
We prove the existence of a conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to plus terms of order where …
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…
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…
A Note on Flux Integrals over Smooth Regular Domains
Ido Bright, John M. Lee
We provide new bounds on a flux integral over the portion of the boundary of one regular domain contained inside a second regular domain, based on properties of the second domain r…