17 citations · 69 across the 14 of their papers we have counts for
20 papers
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.
Semicontinuity of capacity under pointed intrinsic flat convergence
Jeffrey L. Jauregui, Raquel Perales, Jacobus W. Portegies
The concept of the capacity of a compact set in generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multip…
Scalar curvature and the relative capacity of geodesic balls
Jeffrey L. Jauregui
In a Riemannian manifold, it is well known that the scalar curvature at a point can be recovered from the volumes (areas) of small geodesic balls (spheres). We show the scalar curv…
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…
Lower semicontinuity of ADM mass under intrinsic flat convergence
Jeffrey L. Jauregui, Dan A. Lee
A natural question in mathematical general relativity is how the ADM mass behaves as a functional on the space of asymptotically flat 3-manifolds of nonnegative scalar curvature. I…
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…
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…
Lower semicontinuity of mass under convergence and Huisken's isoperimetric mass
Jeffrey L. Jauregui, Dan A. Lee
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed Cheeger--Gromov sense to an asy…
On the lower semicontinuity of the ADM mass
Jeffrey L. Jauregui
The ADM mass, viewed as a functional on the space of asymptotically flat Riemannian metrics of nonnegative scalar curvature, fails to be continuous for many natural topologies. In…
Time flat surfaces and the monotonicity of the spacetime Hawking mass II
Hubert L. Bray, Jeffrey L. Jauregui, Marc Mars
In this sequel paper we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes tha…
On curves with nonnegative torsion
Hubert L. Bray, Jeffrey L. Jauregui
We provide new results and new proofs of results about the torsion of curves in . Let be a smooth curve in that is the graph over a simple closed c…
Time flat surfaces and the monotonicity of the spacetime Hawking mass
Hubert L. Bray, Jeffrey L. Jauregui
We identify a condition on spacelike 2-surfaces in a spacetime that is relevant to understanding the concept of mass in general relativity. We prove a formula for the variation of…
Extensions and fill-ins with nonnegative scalar curvature
Jeffrey Jauregui, Pengzi Miao, Luen-Fai Tam
Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown…
Conformal diffeomorphisms of gradient Ricci solitons and generalized quasi-Einstein manifolds
Jeffrey Jauregui, William Wylie
In this paper we extend some well-known rigidity results for conformal changes of Einstein metrics to the class of generalized quasi-Einstein (GQE) metrics, which includes gradient…
Penrose-type inequalities with a Euclidean background
Jeffrey L. Jauregui
The Riemannian Penrose inequality (RPI) bounds from below the ADM mass of asymptotically flat manifolds of nonnegative scalar curvature in terms of the total area of all outermost…
Fill-ins of nonnegative scalar curvature, static metrics, and quasi-local mass
Jeffrey L. Jauregui
Consider a triple of "Bartnik data" , where is a topological 2-sphere with Riemannian metric and positive function . We view Bartnik data as a boundary conditi…
Invariants of the harmonic conformal class of an asymptotically flat manifold
Jeffrey L. Jauregui
Consider an asymptotically flat Riemannian manifold of dimension with nonempty compact boundary. We recall the harmonic conformal class of the metric, wh…
A geometric theory of zero area singularities in general relativity
Hubert L. Bray, Jeffrey L. Jauregui
The Schwarzschild spacetime metric of negative mass is well-known to contain a naked singularity. In a spacelike slice, this singularity of the metric is characterized by the prope…