On boundary value problems for Einstein metrics

Geometry and Topology

Volumn 12, Issue 4, 2008, Pages 2009-2045

  Anderson, Michael T ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

Einstein metrics; Elliptic boundary; Value problems

Indexed keywords

EID: 66249147696     PISSN: 13640380     EISSN: 13640380     Source Type: Journal    
DOI: 10.2140/gt.2008.12.2009     Document Type: Article

References (19)

1. S Agmon, A Douglis, L Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I and II, Comm. Pure Appl. Math. 12 and 17 (1964) 623-727
2. M Anderson, Geometric aspects of the AdS/CFT correspondence, from: AdS/CFT correspondence: Einstein metrics and their conformal boundaries, IRMA Lect. Math. Theor. Phys. 8, Eur. Math. Soc., Zürich (2005) 1-31 MR2160865
3. M T Anderson, M Herzlich, Unique continuation results for Ricci curvature and applications, J. Geom. Phys. 58 (2008) 179-207 MR2384310
4. M Anderson, A Katsuda, Y Kurylev, M Lassas, M Taylor, Boundary regularity for the Ricci equation, geometric convergence, and Gel'fand's inverse boundary problem, Invent. Math. 158 (2004) 261-321 MR2096795
5. A L Besse, Einstein manifolds, Ergebnisse series 10, Springer (1987) MR867684
6. D G Ebin, The manifold of Riemannian metrics, from: Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer. Math. Soc. (1970) 11-40 MR0267604
7. J Eells, L Lemaire, Deformations of metrics and associated harmonic maps, from: Geometry and analysis, Indian Acad. Sci. (1980) 33-45 MR592252
8. D Gilbarg, N S Trudinger, Elliptic partial differential equations of second order, Grundlehren series 224, Springer (1983) MR737190
9. R S Hamilton, The inverse function theorem of Nash and Moser, Bull. Amer. Math. Soc. (N.S.) 7 (1982) 65-222 MR656198
10. S W Hawking, G F R Ellis, The large scale structure of spacetime, Cambridge University Press (1973) MR0424186 Cambridge Monographs on Mathematical Physics, No. 1
11. S Kobayashi, K Nomizu, Foundations of Differential Geometry, Volume 1, John Wiley, New York (1963)
12. N Koiso, Rigidity and infinitesimal deformability of Einstein metrics, Osaka J. Math. 19 (1982) 643-668 MR676241
13. C LeBrun, M Wang, Surveys in differential geometry: essays on Einstein manifolds, Surveys in Differential Geometry, VI, International Press (1999) MR1798603
14. A Marini, Dirichlet and Neumann boundary value problems for Yang-Mills connections, Comm. Pure Appl. Math. 45 (1992) 1015-1050 MR1168118
15. R Mazzeo, R B Melrose, Pseudodifferential operators on manifolds with fibred boundaries, Asian J. Math. 2 (1998) 833-866 MR1734130
16. C B Morrey, Multiple integrals in the calculus of variations, Grundlehren series 130, Springer, New York (1966) MR0202511
17. J Nash, The imbedding problem for Riemannian manifolds, Ann. of Math. (2) 63 (1956) 20-63 MR0075639
18. L Nirenberg, The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953) 337-394 MR0058265
19. J M Schlenker, Einstein manifolds with convex boundaries, Comment. Math. Helv. 76 (2001) 1-28 MR1819659