@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}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {20}, year = {2001-2002}, mrnumber = {1987634}, zbl = {1038.58043}, language = {en}, url = {http://archive.numdam.org/item/TSG_2001-2002__20__9_0/} }
TY - JOUR AU - Herzlich, Marc TI - Minimal surfaces, the Dirac operator and the Penrose inequality JO - Séminaire de théorie spectrale et géométrie PY - 2001-2002 SP - 9 EP - 16 VL - 20 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/item/TSG_2001-2002__20__9_0/ LA - en ID - TSG_2001-2002__20__9_0 ER -
Herzlich, Marc. Minimal surfaces, the Dirac operator and the Penrose inequality. Séminaire de théorie spectrale et géométrie, Tome 20 (2001-2002), pp. 9-16. http://archive.numdam.org/item/TSG_2001-2002__20__9_0/
[1] Coordinate invariance and energy expressions in General Relativity, Phys. Rev.122 ( 1961), 997-1006. | MR | Zbl
, , and ,[2] Spectral asymmetry and Riemannian geometry I, Math. Proc. Camb. PhD. Soc. 77 ( 1975), 43-69. | MR | Zbl
, , and ,[3] The mass of an asymptotically flat manifold, Commun. Pure. Appl. Math. 39 ( 1986), 661-693. | MR | Zbl
,[4] Proof of the Riemannian Penrose conjecture using the positive mass theorem, J. Difif. Geom ( 2002), to appear. | Zbl
,[5] Curvature estimates and the positive mass theorem, preprint ( 1998). | MR | Zbl
and ,[6] Least area tori and 3-manifolds of nonnegative scalar curvature, Math Z.223 ( 1997), 387-395. | MR | Zbl
and ,[7] Rigidity of area minimizing tori in 3-manifolds of non negative scalar curvature, Comm. Anal. Geom. 8 ( 2000), 565-573. | MR | Zbl
and ,[8] A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds, Commun. Math. Phys. 188 ( 1997), 121-133. | MR | Zbl
,[9] A conformal lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Commun. Math. Phys 104 ( 1986), 151-162. | MR | Zbl
,[10] Première valeur propre de l'opérateur de Dirac et nombre de Yamabe, C.R. Acad. Sci. Paris 313 ( 1991), 865-868. | MR | Zbl
,[11] The inverse mean curvature flow and the Riemannian Penrose inequality, J. Diff. Geom. ( 2002), to appear. | MR | Zbl
and ,[12] The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 ( 1971), 247-258. | MR | Zbl
,[13] On Witten's proof of the positive energy theorem, Commun. Math. Phys. 84 ( 1982), 223-238. | MR | Zbl
and ,[14] Naked singularities, Ann. N.Y. Acad Sci. 224 ( 1973), 125-134. | Zbl
,[15] On the proof of the positive mass conjecture in General Relativity, Commun. Math. Phys 65 ( 1979), 45-76. | MR | Zbl
and ,[16] A new proof of the positive energy theorem, Commun. Math. Phys. 80 ( 1981), 381 -402. | MR | Zbl
,