111 citations · 762 across the 48 of their papers we have counts for
6 papers · 1 filter
Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem
Michael T. Anderson, Atsushi Katsuda, Yaroslav Kurylev +2
This paper explores and ties together three themes. The first is to establish regularity of a metric tensor, on a manifold with boundary, on which there are given Ricci curvature b…
On uniqueness and differentiability in the space of Yamabe metrics
Michael T. Anderson
We prove that generically (positive) Yamabe metrics are unique in their conformal class, and describe some sufficient conditions which imply that a Yamabe metric of locally maximal…
Regularity for Lorentz Metrics under Curvature Bounds
Michael T. Anderson
Let (M, g) be an (n+1) dimensional space-time, with bounded curvature with respect to a bounded framing. If (M, g) is vacuum or satisfies a mild condition on the stress-energy tens…
Cheeger-Gromov Theory and Applications to General Relativity
Michael T. Anderson
This paper surveys aspects of the convergence and degeneration of Riemannian metrics on a given manifold M - the Cheeger-Gromov theory - and extensions thereof to Ricci curvature i…
Scalar curvature and the existence of geometric structures on 3-manifolds, II
Michael T. Anderson
This is a continuation of a previous paper of same title. The degeneration, i.e. curvature blow-up, of sequences of metrics appoaching the Sigma constant, assumed non-positive, is…
Scalar curvature and the existence of geometric structures on 3-manifolds, I
Michael T. Anderson
This paper analyses the convergence and degeneration of sequences of metrics on a 3-manifold, and relations of such with Thurston's geometrization conjecture. The sequences are min…