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Maximum capacity of Bartnik data and a generalization of static metrics
Jeffrey L. Jauregui
Inspired by R. Bartnik's mass minimization problem in general relativity, we investigate a dual problem of maximizing the capacity among asymptotically flat extensions (with nonneg…
A note on Huisken's isoperimetric mass
Jeffrey L. Jauregui, Dan A. Lee, Ryan Unger
In this short note, we explain that Huisken's isoperimetric mass is always nonnegative for elementary reasons.
ADM mass and the capacity-volume deficit at infinity
Jeffrey L. Jauregui
Based on the isoperimetric inequality, G. Huisken proposed a definition of total mass in general relativity that is equivalent to the ADM mass for (smooth) asymptotically flat 3-ma…
Smoothing the Bartnik boundary conditions and other results on Bartnik's quasi-local mass
Jeffrey L. Jauregui
Quite a number of distinct versions of Bartnik's definition of quasi-local mass appear in the literature, and it is not a priori clear that any of them produce the same value in ge…
Lower semicontinuity of the ADM mass in dimensions two through seven
Jeffrey L. Jauregui
The semicontinuity phenomenon of the ADM mass under pointed (i.e., local) convergence of asymptotically flat metrics is of interest because of its connections to nonnegative scalar…