18 citations · 53 across the 8 of their papers we have counts for
8 papers
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…
Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries
Michael Holst, Caleb Meier
In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Buil…
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…
Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries
M. Holst, C. Meier, G. Tsogtgerel
In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds wi…
An Alternative Between Non-unique and Negative Yamabe Solutions to the Conformal Formulation of the Einstein Constraint Equations
Michael Holst, Caleb Meier
The conformal method has been effective for parametrizing solutions to the Einstein constraint equations on closed 3-manifolds. However, it is still not well-understood; for exampl…
Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables
Harry Dym, J. W. Helton, Caleb Meier
Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non…
Non-uniqueness of Solutions to the Conformal Formulation
Michael Holst, Caleb Meier
It is well-known that solutions to the conformal formulation of the Einstein constraint equations are unique in the cases of constant mean curvature (CMC) and near constant mean cu…
Generalized Solutions to Semilinear Elliptic PDE with Applications to the Lichnerowicz Equation
Michael Holst, Caleb Meier
In this article we investigate the existence of a solution to a semilinear, elliptic, partial differential equation with distributional coefficients and data. The problem we consid…