Minimal surfaces, the Dirac operator and the Penrose inequality

Marc Herzlich

Séminaire de théorie spectrale et géométrie (2001-2002)

  • Volume: 20, page 9-16
  • ISSN: 1624-5458

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Herzlich, Marc. "Minimal surfaces, the Dirac operator and the Penrose inequality." Séminaire de théorie spectrale et géométrie 20 (2001-2002): 9-16. <http://eudml.org/doc/114468>.

@article{Herzlich2001-2002,
author = {Herzlich, Marc},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {minimal surfaces; Dirac operator; Penrose inequality; positive mass theorem; asymptotically flat spacetimes; Yamabe invariant},
language = {eng},
pages = {9-16},
publisher = {Institut Fourier},
title = {Minimal surfaces, the Dirac operator and the Penrose inequality},
url = {http://eudml.org/doc/114468},
volume = {20},
year = {2001-2002},
}

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
PB - Institut Fourier
VL - 20
SP - 9
EP - 16
LA - eng
KW - minimal surfaces; Dirac operator; Penrose inequality; positive mass theorem; asymptotically flat spacetimes; Yamabe invariant
UR - http://eudml.org/doc/114468
ER -

References

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  3. [3] R. BARTNIK, The mass of an asymptotically flat manifold, Commun. Pure. Appl. Math. 39 ( 1986), 661-693. Zbl0598.53045MR849427
  4. [4] H. BRAY, Proof of the Riemannian Penrose conjecture using the positive mass theorem, J. Difif. Geom ( 2002), to appear. Zbl1039.53034
  5. [5] H. BRAY and F. FINSTER, Curvature estimates and the positive mass theorem, preprint ( 1998). Zbl1030.53041MR1900753
  6. [6] M. CAI and G. GALLOWAY, Least area tori and 3-manifolds of nonnegative scalar curvature, Math Z.223 ( 1997), 387-395. Zbl0869.53035MR1417850
  7. [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. Zbl0994.53028MR1775139
  8. [8] M. HERZLICH, A Penrose-like inequality for the mass of Riemannian asymptotically flat manifolds, Commun. Math. Phys. 188 ( 1997), 121-133. Zbl0886.53032MR1471334
  9. [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. Zbl0593.58040MR834486
  10. [10] O. HIJAZI, Première valeur propre de l'opérateur de Dirac et nombre de Yamabe, C.R. Acad. Sci. Paris 313 ( 1991), 865-868. Zbl0738.53030MR1138566
  11. [11] G. HUISKEN and T. ILMANEN, The inverse mean curvature flow and the Riemannian Penrose inequality, J. Diff. Geom. ( 2002), to appear. Zbl1055.53052MR1916951
  12. [12] M. OBATA, The conjectures on conformal transformations of Riemannian manifolds, J. Diff. Geom. 6 ( 1971), 247-258. Zbl0236.53042MR303464
  13. [13] T.H. PARKER and C.H. TAUBES, On Witten's proof of the positive energy theorem, Commun. Math. Phys. 84 ( 1982), 223-238. Zbl0528.58040MR661134
  14. [14] R. PENROSE, Naked singularities, Ann. N.Y. Acad Sci. 224 ( 1973), 125-134. Zbl0925.53023
  15. [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. Zbl0405.53045MR526976
  16. [16] E. WITTEN, A new proof of the positive energy theorem, Commun. Math. Phys. 80 ( 1981), 381 -402. Zbl1051.83532MR626707

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