Boundaries of zero scalar curvature in the AdS/CFT correspondence

Advances in Theoretical and Mathematical Physics

Volumn 3, Issue 6, 1999, Pages 1-12

  Cai, Mingliang ^a   Galloway, Gregory J ^a  

^a Department of Biology   (United States)

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[No Author keywords available]

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EID: 79551532111     PISSN: 10950761     EISSN: 10950753     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. U. Abresch, Lower curvature bounds, Toponogov's theorem, and bounded topology, Ann. Sci. Ècole Norm. Sup.(4) 18 (1985) 651-670.
2. A. Ashtekar and A. Magnon, Asymptotically anti-de Sitter space-times, Class. Quantum Grav. 1 (1984) L39-L44.
3. A.L. Besse, Einstein manifolds, Springer-Verlag, Berlin, 1987.
4. J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Diff. Geom. 6 (1971) 119-128.
5. C. Croke and B. Kleiner, A warped product splitting theorem, Duke Math. J. 67 (1992) 571-574.
6. J.H. Eschenburg and E. Heintze, An elementary proof of the Cheeger-Gromoll splitting theorem, Ann. Global Anal. Geom. 2 (1984) 141-151.
7. G. Galloway, K. Schleich, D. Witt, and E. Woolgar, Topolgical censorship and higher genus black holes, Phys. Rev. D 60 (1999) 104039.
8. The AdS/CFT correspondence conjecture and topological censorship, preprint.
9. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, 2nd edition, Springer-Verlag, Berlin, 1983.
10. C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, preprint.
11. H. Karcher, Riemannian comparison constructions, Global Differential Geometry, 170-222, MAA Stud. Math., vol 27, Math. Assoc. America, Washington, DC, 1989.
12. A. Kasue, Ricci curvature, geodesics and some geometric properties of Riemannian man-ifolds with boundary, J. Math. Soc. Japan 35 (1983) 117-131.
13. J. Kazdan and F.W.Warner, Scalar curvature and conformal deformation of Riemannian structure, J. Diff. Geom. 10 (1975) 113-134.
14. W.S. Massey, A basic course in algebraic topology. Graduate Texts in Mathematics, 127, Springer-Verlag, New York, 1991.
15. R. Penrose and W. Rindler, Spinors and Spacetime, vol. 2, chapter 9, Cambridge Uni-versity Press, Cambridge, 1986.
16. E. Witten and S.-T. Yau, Connectedness of the boundary in the AdS/CFT correspon-dence, preprint.
17. H. Wu, An elementary method in the study of nonnegative curvature, Acta Math. 142 (1979) 57-78.