129 citations · 1.9k across the 73 of their papers we have counts for
80 papers
A Numerical Study of the Expanding Direction of -Symmetric Spacetimes
Beverly K. Berger, James Isenberg, Adam Layne
The asymptotic behavior of expanding, generic, -Symmetric, vacuum spacetimes is examined via numerical simulations. After validation of the numerical methods, the properties o…
Convergence stability for Ricci flow on manifolds with bounded geometry
Eric Bahuaud, Christine Guenther, James Isenberg +1
We prove that the Ricci flow for complete metrics with bounded geometry depends continuously on initial conditions for finite time with no loss of regularity. This relies on our re…
A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup: II
David Garfinkle, James Isenberg, Dan Knopf +1
In previous work [GIKW21], we have presented evidence from numerical simulations that the Type-II singularities of mean curvature flow (MCF) of rotationally-symmetric, complete, no…
Sectoriality of the Laplacian on Asymptotically Hyperbolic Spaces
Eric Bahuaud, Christine Guenther, James Isenberg
We prove that both the Laplacian on functions, and the Lichnerowicz Laplacian on symmetric 2-tensors with respect to asymptotically hyperbolic metrics, are sectorial maps in weight…
Stability of Asymptotic Behavior Within Polarised -Symmetric Vacuum Solutions with Cosmological Constant
Ellery Ames, Florian Beyer, James Isenberg +1
We prove the nonlinear stability of the asymptotic behavior of perturbations of subfamilies of Kasner solutions in the contracting time direction within the class of polarised $T^2…
A Phase Space Approach to the Conformal Construction of Non-Vacuum Initial Data Sets in General Relativity
James Isenberg, David Maxwell
We present a uniform (and unambiguous) procedure for scaling the matter fields in implementing the conformal method to parameterize and construct solutions of Einstein constraint e…