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On Witten’s proof of the positive energy theorem. (English) Zbl 0528.58040


MSC:

58J90 Applications of PDEs on manifolds
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
53C80 Applications of global differential geometry to the sciences

Citations:

Zbl 0405.53045
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References:

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[3] Cantor, M.: Some problems of global analysis on asymptotically simple manifolds. Compositio Math.38, 3-35 (1979) · Zbl 0402.58004
[4] Choquet-Bruhat, Y., Christodoulou, D.: Elliptic systems inH s,? spaces on manifolds which are Euclidean at infinity. Acta. Math.146, 124-150 (1981) · Zbl 0484.58028 · doi:10.1007/BF02392460
[5] Geroch, R.: General relativity. Proc. Symp. Pure Math.27, 401-414 (1975) · Zbl 0307.53038
[6] Hawking, S., Ellis, G.: The large scale structure of space-time. Cambridge: Cambridge University Press 1973 · Zbl 0265.53054
[7] Hitchen, N.: Harmonic spinors. Adv. Math.14, 1-55 (1974) · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8
[8] Morrey, C. B.: Multiple integrals in the calculus of variations. New York: Springer 1966 · Zbl 0142.38701
[9] Nirenberg, L., Walker, H.: The null spaces of elliptic partial differential operators in ? N . J. Math. Anal. App.47, 271-301 (1973) · Zbl 0272.35029 · doi:10.1016/0022-247X(73)90138-8
[10] Schoen, R., Yau, S.-T.: On the proof of the positive mass conjecture in general relativity. Commun. Math. Phys.65, 45-76 (1976). · Zbl 0405.53045 · doi:10.1007/BF01940959
[11] Schoen, R., Yau, S.-T.: Positivity of the total mass in a general space-time. Phys. Rev. Lett.43, 1457-1459 (1979) · doi:10.1103/PhysRevLett.43.1457
[12] Schoen, R., Yau, S.-T.: Proof of the positive mass theorem II. Commun. Math. Phys.79, 231 (1981) · Zbl 0494.53028 · doi:10.1007/BF01942062
[13] Schoen, R., Yau, S.-T.: The energy and the linear momentum of space-times in general relativity. Commun. Math. Phys.79, 47 (1981). · Zbl 0934.83031 · doi:10.1007/BF01208285
[14] Vainberg, M.: Variational methods and the method of monotone operators in the theory of nonlinear equations. New York: Wiley 1973 · Zbl 0279.47022
[15] Witten, E.: A simple proof of the positive energy theorem. Commun. Math. Phys.80, 381-402 (1931) · Zbl 1051.83532 · doi:10.1007/BF01208277
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