111 citations · 762 across the 48 of their papers we have counts for
33 papers · 1 filter
The Bartnik quasi-local mass conjectures
Michael T. Anderson
This paper is a tribute to Robert Bartnik and his work and conjectures on quasi-local mass. We present a framework in which to clearly analyse Bartnik's static vacuum extension con…
Recent progress and problems on the Bartnik quasi-local mass
Michael T. Anderson
This paper surveys recent progress on issues related to the Bartnik quasi-local mass . In addition, we formulate a number of new problems and conjectures regarding foundationa…
The Nirenberg problem of prescribed Gauss curvature on
Michael T. Anderson
We introduce a new perspective on the classical Nirenberg problem of understanding the possible Gauss curvatures of metrics on conformal to the round metric. A key tool is…
Elliptic regularization of the isometric immersion problem
Michael T. Anderson
We introduce an elliptic regularization of the PDE system representing the isometric immersion of a surface in . The regularization is geometric, and has a natural v…
Embeddings, immersions and the Bartnik quasi-local mass conjectures
Michael T. Anderson, Jeffrey L. Jauregui
Given a Riemannian 3-ball of non-negative scalar curvature, Bartnik conjectured that admits an asymptotically flat (AF) extension (without horizons) of…
On the Bartnik conjecture for the static vacuum Einstein equations
Michael T. Anderson
We prove that given any smooth metric and smooth positive function on , there is a constant , depending on , and an asymptotically flat solution $(M, g…