9 citations · 31 across the 8 of their papers we have counts for
8 papers
When Do Spacetimes Have Constant Mean Curvature Slices?
James Dilts, Michael Holst
Many results in mathematical relativity, including results for both the initial data problem and for the evolution problem, rely on the existence of a constant mean curvature (CMC)…
Numerical Bifurcation Analysis of the Conformal Method
James Dilts, Michael Holst, Tamara Kozareva +1
The conformal formulation of the Einstein constraint equations has been studied intensively since the modern version of the conformal method was first pub- lished in the early 1970…
Existence and Blowup Results for Asymptotically Euclidean Initial Data Sets Generated by the Conformal Method
James Dilts, James Isenberg
For each set of (freely chosen) seed data, the conformal method reduces the Einstein constraint equations to a system of elliptic equations, the conformal constraint equations. We…
The Einstein Constraint Equations on Asymptotically Euclidean Manifolds
James Dilts
In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and suf…
Yamabe Classification and Prescribed Scalar Curvature in the Asymptotically Euclidean Setting
David Maxwell, James Dilts
We prove a necessary and sufficient condition for an asymptotically Euclidean manifold to be conformally related to one with specified nonpositive scalar curvature: the zero set of…
A limit equation criterion for applying the conformal method to asymptotically cylindrical initial data sets
James Dilts, Jeremy Leach
We prove that in a certain class of conformal data on an asymptotically cylindrical manifold, if the conformally decomposed Einstein constraint equations do not admit a solution, t…
Non-CMC solutions of the Einstein constraint equations on asymptotically Euclidean manifolds
James Dilts, James Isenberg, Rafe Mazzeo +1
In this note we prove two existence theorems for the Einstein constraint equations on asymptotically Euclidean manifolds. The first is for arbitrary mean curvature functions with r…
The Einstein Constraint Equations on Compact Manifolds with Boundary
James Dilts
We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and prov…