PROOF OF THE RIEMANNIAN PENROSE INEQUALITY USING THE POSITIVE MASS THEOREM

By H. Bray. 2001

516 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b09c0a9037d77f0d355c830444dc524c710c7157

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. A. Neves
2. S. Brendle
3. M. Mars
4. Chao Xia
5. H. Bray
6. G. Huisken
7. Dan A. Lee
8. Junfang Li

In Astronomy and Astrophysics

1. Mihalis Dafermos
2. M. Mars
3. A. Neves
4. Abhay Ashtekar
5. Igor Rodnianski
6. B. Krishnan
7. H. Bray
8. Dan A. Lee

In Nuclear and High Energy Physics

1. M. Mars
2. Igor Rodnianski
3. Abhay Ashtekar
4. A. Neves
5. Mihalis Dafermos
6. B. Krishnan
7. T. Ilmanen
8. Dan A. Lee

Citations in the corpus

• An integral formula and its applications on sub-static manifolds (2016, background): “These inner boundaries are typically horizons, see the definition of horizons in [1].”
• The inverse mean curvature flow and the Riemannian Penrose Inequality (2001, methodology): “The positive scalar curvature of M corresponds to the physical hypothesis of nonnegative energy density on L, expressed by the so(1)Using a novel and surprising technique, Bray [12] has recently proven the most general form of the Riemannian Penrose Inequality, namely 16πm(2) ≥ |∂M | with no connect”
• Isolated and Dynamical Horizons and Their Applications (2004, background): “The conjecture has been proved in time symmetric situations relatively recently [101, 52].”
• Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds (2007, methodology): “Introduction A Penrose inequality for asymptotically flat 3-manifolds was proven independently by Huisken-Ilmanen [5], using inverse mean curvature flow, and Hugh Bray [1], using a conformal deformation of the ambient metric.”
• The 1965 Penrose singularity theorem (2014, background): “general case, and even in spherical symmetry only a weaker version |using the energy rather than the mass| has been shown to hold [177]. However, (14) has been proven in the so-called Riemannian case [185, 47] which, from the space-time viewpoint, describes a time-symmetric situation, using the slic”
• The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass (2013, methodology): “Bray [3] later proved the more general inequality described above using a different method, and this result was later extended to dimensions less than 8 by Bray and the first author [4].”
• Minimal submanifolds (2005, unknown): “See, for instance, [9] and [47] for some results on black holes, horizons, etc.”
• Present status of the Penrose inequality (2009, methodology): “This result, also due to Bray [22], has independent interest and has been already used in another context by P.”
• Rigidity of area-minimizing two-spheres in three-manifolds (2010, methodology): “The use of constant mean curvature surfaces is motivated in part by work of Bray [1] and Huisken and Yau [10] (see also [2] and [9]).”
• The evolution problem in general relativity (2008, background): “See the important papers of Huisken-Ilmanen [86] and Bray [22].”
• Lectures on black holes and linear waves (2008, background): “See the important papers of HuiskenIlmanen [95] and Bray [25].”