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of 51
pro vyhledávání: '"Jauregui, Jeffrey L."'
In this short note, we explain that Huisken's isoperimetric mass is always nonnegative for elementary reasons.
Comment: 5 pages + references
Comment: 5 pages + references
Externí odkaz:
http://arxiv.org/abs/2408.08871
The concept of the capacity of a compact set in $\mathbb R^n$ generalizes readily to noncompact Riemannian manifolds and, with more substantial work, to metric spaces (where multiple natural definitions of capacity are possible). Motivated by analyti
Externí odkaz:
http://arxiv.org/abs/2204.09732
Autor:
Jauregui, Jeffrey L.
Publikováno v:
Proc. Amer. Math. Soc., Vol 149, No. 11, (2021), pp. 4907--4921
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 curvature is likewise determined by the relative capacities of concentric
Externí odkaz:
http://arxiv.org/abs/2009.12394
Autor:
Jauregui, Jeffrey L.
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-manifolds of nonnegative scalar curvature, but that is well-defined in g
Externí odkaz:
http://arxiv.org/abs/2002.08941
Autor:
Jauregui, Jeffrey L., Lee, Dan A.
Publikováno v:
Calculus of Variations and Partial Differential Equations, Vol 60, No. 2 (2021)
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. In previous results, lower semicontinuity has been established by the f
Externí odkaz:
http://arxiv.org/abs/1903.00916
Autor:
Jauregui, Jeffrey L.
Publikováno v:
J. Geom. Phys., Vol. 136 (2019), pg. 228-243
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 general. In this paper we make progress on reconciling these definitions
Externí odkaz:
http://arxiv.org/abs/1806.08348
Autor:
Jauregui, Jeffrey L.
Publikováno v:
Pacific J. Math. 301 (2019) 441-466
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 curvature, the positive mass theorem, and Bartnik's mass-minimization
Externí odkaz:
http://arxiv.org/abs/1804.04723
Publikováno v:
Ann. Henri Poincar\'e, Vol. 20, No. 5 (2019), pg. 1651--1698
Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF s
Externí odkaz:
http://arxiv.org/abs/1611.08755
Autor:
Jauregui, Jeffrey L., Lee, Dan A.
Publikováno v:
Journal fuer die reine und angewandte Mathematik (Crelle's Journal), Vol. 2019, No. 756, pg. 227-257
Given a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed $C^0$ Cheeger--Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit
Externí odkaz:
http://arxiv.org/abs/1602.00732
Autor:
Jauregui, Jeffrey L.
Publikováno v:
Comm. Anal. Geom., Vol. 26, No. 1, 2018
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 this paper we prove that lower semicontinuity holds in natural setting
Externí odkaz:
http://arxiv.org/abs/1411.3699