Minimal surfaces, the Dirac operator and the Penrose inequality
Séminaire de théorie spectrale et géométrie, Tome 20 (2001-2002), pp. 9-16 
@article{TSG_2001-2002__20__9_0,
     author = {Herzlich, Marc},
     title = {Minimal surfaces, the {Dirac} operator and the {Penrose} inequality},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {9--16},
     year = {2001-2002},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {20},
     mrnumber = {1987634},
     zbl = {1038.58043},
     language = {en},
     url = {https://www.numdam.org/item/TSG_2001-2002__20__9_0/}
}
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Herzlich, Marc. Minimal surfaces, the Dirac operator and the Penrose inequality. Séminaire de théorie spectrale et géométrie, Tome 20 (2001-2002), pp. 9-16. https://www.numdam.org/item/TSG_2001-2002__20__9_0/

[1] R. Arnowitt, S. Deser, and C.W. Misner, Coordinate invariance and energy expressions in General Relativity, Phys. Rev.122 ( 1961), 997-1006. | Zbl | MR

[2] M. Fatiyah, V.K. Patodi, and I.M. Singer, Spectral asymmetry and Riemannian geometry I, Math. Proc. Camb. PhD. Soc. 77 ( 1975), 43-69. | Zbl | MR

[3] R. Bartnik, The mass of an asymptotically flat manifold, Commun. Pure. Appl. Math. 39 ( 1986), 661-693. | Zbl | MR

[4] H. Bray, Proof of the Riemannian Penrose conjecture using the positive mass theorem, J. Difif. Geom ( 2002), to appear. | Zbl

[5] H. Bray and F. Finster, Curvature estimates and the positive mass theorem, preprint ( 1998). | Zbl | MR

[6] M. Cai and G. Galloway, Least area tori and 3-manifolds of nonnegative scalar curvature, Math Z.223 ( 1997), 387-395. | Zbl | MR

[7] M. Cai and G. Galloway, Rigidity of area minimizing tori in 3-manifolds of non negative scalar curvature, Comm. Anal. Geom. 8 ( 2000), 565-573. | Zbl | MR

[8] M. Herzlich, A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds, Commun. Math. Phys. 188 ( 1997), 121-133. | Zbl | MR

[9] O. Hijazi, A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Commun. Math. Phys 104 ( 1986), 151-162. | Zbl | MR

[10] O. Hijazi, Première valeur propre de l'opérateur de Dirac et nombre de Yamabe, C.R. Acad. Sci. Paris 313 ( 1991), 865-868. | Zbl | MR

[11] G. Huisken and T. Ilmanen, The inverse mean curvature flow and the Riemannian Penrose inequality, J. Diff. Geom. ( 2002), to appear. | Zbl | MR

[12] M. Obata, The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 ( 1971), 247-258. | Zbl | MR

[13] T.H. Parker and C.H. Taubes, On Witten's proof of the positive energy theorem, Commun. Math. Phys. 84 ( 1982), 223-238. | Zbl | MR

[14] R. Penrose, Naked singularities, Ann. N.Y. Acad Sci. 224 ( 1973), 125-134. | Zbl

[15] R. Schoen and S.T. Yau, On the proof of the positive mass conjecture in General Relativity, Commun. Math. Phys 65 ( 1979), 45-76. | Zbl | MR

[16] E. Witten, A new proof of the positive energy theorem, Commun. Math. Phys. 80 ( 1981), 381 -402. | Zbl | MR