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Volumn 59, Issue 2, 2001, Pages 177-267

Proof of the riemannian penrose inequality using the positive mass theorem

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EID: 0035497450     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1090349428     Document Type: Article
Times cited : (440)

References (53)
  • 1
    • 0000177308 scopus 로고
    • Coordinate Invariance and Energy Expressions in General Relativity
    • R. Arnowitt, S. Deser, & C. Misner, Coordinate Invariance and Energy Expressions in General Relativity, Phys. Rev. 122 (1961) 997-1006.
    • (1961) Phys. Rev , vol.122 , pp. 997-1006
    • Arnowitt, R.1    Deser, S.2    Misner, C.3
  • 2
    • 84990556234 scopus 로고
    • The Mass of an Asymptotically Flat Manifold
    • R. Bartnik, The Mass of an Asymptotically Flat Manifold, Comm. Pure Appl. Math. 39 (1986) 661-693.
    • (1986) Comm. Pure Appl. Math , vol.39 , pp. 661-693
    • Bartnik, R.1
  • 3
    • 0001310730 scopus 로고
    • New Definition of Quasi-Local Mass
    • R. Bartnik, New Definition of Quasi-Local Mass, Phys. Rev. Lett. 62 (1989) 2346.
    • (1989) Phys. Rev. Lett , vol.62 , pp. 2346
    • Bartnik, R.1
  • 4
    • 84972545815 scopus 로고
    • Quasi-Spherical Metrics and Prescribed Scalar Curvature
    • R. Bartnik, Quasi-Spherical Metrics and Prescribed Scalar Curvature, J. Differential Geom. 37 (1993) 31-71.
    • (1993) J. Differential Geom , vol.37 , pp. 31-71
    • Bartnik, R.1
  • 6
    • 0031524464 scopus 로고    scopus 로고
    • On the Penrose Inequality and the Role of Auxiliary Spinor Fields, Class
    • G. Bergquist, On the Penrose Inequality and the Role of Auxiliary Spinor Fields, Class. Quantum Grav. 14 (1997) 2577-2583.
    • (1997) Quantum Grav , vol.14 , pp. 2577-2583
    • Bergquist, G.1
  • 7
    • 0003497848 scopus 로고    scopus 로고
    • The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature
    • Stanford University
    • H.L. Bray, The Penrose Inequality in General Relativity and Volume Comparison Theorems Involving Scalar Curvature, thesis, Stanford University, 1997.
    • (1997) Thesis
    • Bray, H.L.1
  • 9
  • 10
  • 11
    • 33751567593 scopus 로고
    • Non-Existence of Multiple Black Holes in Asymptotically Euclidean, Static Vacuum Space-Time
    • Bunting B. & Masood-ul-Alam, M. Non-Existence of Multiple Black Holes in Asymptotically Euclidean, Static Vacuum Space-Time, Gen. Rel. and Grav. 19(2) (1987).
    • (1987) Gen. Rel. and Grav , vol.19 , Issue.2
    • Bunting, B.1    Masood-Ul-Alam, M.2
  • 12
    • 0012623859 scopus 로고    scopus 로고
    • Rigidity of Area Minimizing Tori in 3-Manifolds of Nonnegative Scalar Curvature
    • M. Cai and G. Galloway, Rigidity of Area Minimizing Tori in 3-Manifolds of Nonnegative Scalar Curvature, Comm. in Anal. and Geom., to appear, math.DG/9804096.
    • Comm. in Anal. and Geom
    • Cai, M.1    Galloway, G.2
  • 13
    • 0001867432 scopus 로고
    • Examples of Naked Singularity Formation in the Gravitational Collapse of a Scalar Field
    • D. Christodoulou, Examples of Naked Singularity Formation in the Gravitational Collapse of a Scalar Field, Ann. of Math. 140 (1994) 607-653.
    • (1994) Ann. of Math. , vol.140 , pp. 607-653
    • Christodoulou, D.1
  • 17
    • 0032352461 scopus 로고    scopus 로고
    • Local U(2,2) Symmetry in Relativistic Quantum Mechanics, hep-th/9703083
    • F. Finster, Local U(2,2) Symmetry in Relativistic Quantum Mechanics, hep-th/9703083, J. Math. Phys. 39 (1998) 6276-6290.
    • (1998) J. Math. Phys , vol.39 , pp. 6276-6290
    • Finster, F.1
  • 18
  • 19
    • 0031519527 scopus 로고    scopus 로고
    • Collapsing Shells and the Isoperimetric Inequality for Black Holes
    • G. Gibbons, Collapsing Shells and the Isoperimetric Inequality for Black Holes, Class. Quant. Grav. 14 (1997) 2905.
    • (1997) Class. Quant. Grav , vol.14 , pp. 2905
    • Gibbons, G.1
  • 22
    • 0000280956 scopus 로고
    • Gravitational Radiation in an Expanding Universe
    • S.W. Hawking, Gravitational Radiation in an Expanding Universe, J. Math. Phys. 9 (1968) 598-604.
    • (1968) J. Math. Phys , vol.9 , pp. 598-604
    • Hawking, S.W.1
  • 23
    • 33744571220 scopus 로고
    • Black Holes in General Relativity, Comm
    • S.W. Hawking, Black Holes in General Relativity, Comm. Math. Phys. 25 (1972) 152-166.
    • (1972) Math. Phys , vol.25 , pp. 152-166
    • Hawking, S.W.1
  • 25
    • 0014929453 scopus 로고
    • The Singularities of Gravitational Collapse and Cosmology
    • S.W. Hawking & R. Penrose, The Singularities of Gravitational Collapse and Cosmology, Proc. Roy. Soc. A 314 (1970) 529-548.
    • (1970) Proc. Roy. Soc. A , vol.314 , pp. 529-548
    • Hawking, S.W.1    Penrose, R.2
  • 26
    • 0031536628 scopus 로고    scopus 로고
    • A Penrose-like Inequality for the Mass of Riemannian Asymptotically Flat Manifolds
    • M. Herzlich, A Penrose-like Inequality for the Mass of Riemannian Asymptotically Flat Manifolds, Comm. Math. Phys. 188 (1997) 121.
    • (1997) Comm. Math. Phys , vol.188 , pp. 121
    • Herzlich, M.1
  • 30
    • 0012713330 scopus 로고    scopus 로고
    • The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality
    • appear
    • G. Huisken & T. Ilmanen, The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality, J. Differential Geom., to appear.
    • J. Differential Geom
    • Huisken, G.1    Ilmanen, T.2
  • 31
    • 1842627896 scopus 로고    scopus 로고
    • The Riemannian Penrose Inequality
    • G. Huisken & T. Ilmanen, The Riemannian Penrose Inequality, Int. Math. Res. Not. 20 (1997) 1045-1058; http://www.math.nwu.edu/∼ilmanen.
    • (1997) Int. Math. Res. Not , vol.20 , pp. 1045-1058
    • Huisken, G.1    Ilmanen, T.2
  • 33
    • 0000948294 scopus 로고
    • On the Positive Energy Conjecture
    • P.S. Jang, On the Positive Energy Conjecture, J. Math. Phys. 17 (1976) 141-145.
    • (1976) J. Math. Phys , vol.17 , pp. 141-145
    • Jang, P.S.1
  • 34
    • 34250800174 scopus 로고
    • On the Positivity of Energy in General Relativity
    • P.S. Jang, On the Positivity of Energy in General Relativity, J. Math. Phys. 19 (1978) 1152-1155.
    • (1978) J. Math. Phys , vol.19 , pp. 1152-1155
    • Jang, P.S.1
  • 35
    • 0001396461 scopus 로고
    • Note on Cosmic Censorship
    • P.S. Jang, Note on Cosmic Censorship, Phys. Rev. Lett. D 20 (1979) 834-838.
    • (1979) Phys. Rev. Lett. D , vol.20 , pp. 834-838
    • Jang, P.S.1
  • 36
    • 0001504885 scopus 로고
    • On the Positivity of the Mass for Black Hole Space-Times
    • P.S. Jang, On the Positivity of the Mass for Black Hole Space-Times, Comm. Math. Phys. 69 (1979) 257-266.
    • (1979) Comm. Math. Phys , vol.69 , pp. 257-266
    • Jang, P.S.1
  • 37
    • 36749114970 scopus 로고
    • The Positive Energy Conjecture and the Cosmic Censor Hypothesis
    • P.S. Jang & R.M. Wald, The Positive Energy Conjecture and the Cosmic Censor Hypothesis, J. Math. Phys. 18 (1977) 41-44.
    • (1977) J. Math. Phys , vol.18 , pp. 41-44
    • Jang, P.S.1    Wald, R.M.2
  • 39
    • 0013478565 scopus 로고
    • Minimal Surfaces of Codimension One
    • Elsevier Science Publishing
    • U. Massari & M. Miranda, Minimal Surfaces of Codimension One, North-Holland mathematics studies, 91, Elsevier Science Publishing, 1984.
    • (1984) North-Holland Mathematics Studies , vol.91
    • Massari, U.1    Miranda, M.2
  • 40
    • 0001180073 scopus 로고
    • On Witten’s Proof of the Positive Energy Theorem
    • T.H. Parker & C.H. Taubes, On Witten’s Proof of the Positive Energy Theorem, Commun. Math. Phys. 84 (1982) 223-238.
    • (1982) Commun. Math. Phys , vol.84 , pp. 223-238
    • Parker, T.H.1    Taubes, C.H.2
  • 41
  • 42
    • 0001107969 scopus 로고
    • Variational Theory for the Total Scalar Curvature Functional for Rie-mannian Metrics and Related Topics
    • (M. Gi-aquinta, ed.) Lecture Notes in Math. 1365, Springer, Berlin
    • R. Schoen, Variational Theory for the Total Scalar Curvature Functional for Rie-mannian Metrics and Related Topics, Topics in Calculus of Variations (M. Gi-aquinta, ed.) Lecture Notes in Math. 1365 120-154, Springer, Berlin, 1987.
    • (1987) Topics in Calculus of Variations , pp. 120-154
    • Schoen, R.1
  • 43
    • 0001593830 scopus 로고
    • Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-negative Scalar Curvature
    • R. Schoen & S.-T. Yau, Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-negative Scalar Curvature, Annals of Mathematics 110 (1979) 127-142.
    • (1979) Annals of Mathematics , vol.110 , pp. 127-142
    • Schoen, R.1    Yau, S.-T.2
  • 44
    • 34250263023 scopus 로고
    • On the Proof of the Positive Mass Conjecture in General Relativity
    • R. Schoen & S.-T. Yau, On the Proof of the Positive Mass Conjecture in General Relativity, Comm. Math. Phys. 65 (1979) 45-76.
    • (1979) Comm. Math. Phys , vol.65 , pp. 45-76
    • Schoen, R.1    Yau, S.-T.2
  • 45
    • 25744453267 scopus 로고
    • Positivity of the Total Mass of a General Space-Time
    • R. Schoen & S.-T. Yau, Positivity of the Total Mass of a General Space-Time, Phys. Rev. Lett. 43 (1979) 1457-1459.
    • (1979) Phys. Rev. Lett , vol.43 , pp. 1457-1459
    • Schoen, R.1    Yau, S.-T.2
  • 46
    • 29244463784 scopus 로고
    • Proof of the Positive Mass TheoremII
    • R. Schoen & S.-T. Yau, Proof of the Positive Mass Theorem II, Comm. Math. Phys. 79 (1981) 231-260.
    • (1981) Comm. Math. Phys , vol.79 , pp. 231-260
    • Schoen, R.1    Yau, S.-T.2
  • 47
    • 0002081241 scopus 로고
    • The Energy and the Linear Momentum of Space-Times in General Relativity
    • R. Schoen & S.-T. Yau, The Energy and the Linear Momentum of Space-Times in General Relativity, Comm. Math. Phys. 79 (1981) 47-51.
    • (1981) Comm. Math. Phys , vol.79 , pp. 47-51
    • Schoen, R.1    Yau, S.-T.2
  • 48
    • 0000699811 scopus 로고
    • The Existence of a Black Hole due to Condensation of Matter
    • R. Schoen & S.-T. Yau, The Existence of a Black Hole due to Condensation of Matter, Comm. Math. Phys. 90 (1983) 575-579.
    • (1983) Comm. Math. Phys , vol.90 , pp. 575-579
    • Schoen, R.1    Yau, S.-T.2
  • 49
    • 0000526405 scopus 로고
    • Existence of Surfaces Minimizing the Willmore Functional
    • L. Simon, Existence of Surfaces Minimizing the Willmore Functional, Comm. Anal. Geom. 1(2) (1993) 281-326.
    • (1993) Comm. Anal. Geom , vol.1 , Issue.2 , pp. 281-326
    • Simon, L.1
  • 51
    • 0003023464 scopus 로고
    • Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations
    • K. Widman, Inequalities for the Green Function and Boundary Continuity of the Gradient of Solutions of Elliptic Differential Equations, Math. Scand. 21 (1967) 17-37.
    • (1967) Math. Scand , vol.21 , pp. 17-37
    • Widman, K.1
  • 52
    • 33744727108 scopus 로고
    • A New Proof of the Positive Energy Theorem
    • E. Witten, A New Proof of the Positive Energy Theorem, Comm. Math. Phys. 80 (1981) 381-402.
    • (1981) Comm. Math. Phys , vol.80 , pp. 381-402
    • Witten, E.1


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