The regularity of the solutions to the Yamabe Problem is considered in the case of conformally compact manifolds and negative scalar curvature. The existence of smooth hyperboloidal initial data for Einstein's field equations is demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Access this article Subscribe and saveSpringer+ Basic
€34.99 /Month
Price includes VAT (Germany)
Instant access to the full article PDF.
Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. ReferencesAndersson, L.: Elliptic systems on manifolds with asymptotically negative curvature. Submitted at Indiana Univ. Math. J. 1990
Andersson, L., Chruściel, P. T.: In preparation
Aviles, P., McOwen, R. C.: Complete conformal metrics with negative scalar curvature in compact Riemannian manifolds. Duke Math. J.56, 395–398 (1988)
Aviles, P., McOwen, R. C.: Conformal deformation to constant negative scalar curvature on noncompact Riemannian manifolds. J. Differ. Geom.27, 225–239 (1988)
Besse, A. L.: Einstein manifolds, Vol.10 (Ergebnisse der Math.3 Folge) Berlin, Heidelberg, New York: Springer 1987
Friedrich, H.: On static and radiative spacetimes. Commun. Math. Phys.119, 51–73 (1988)
Friedrich, H.: On the global existence and the asymptotic behaviour of solutions to the Einstein-Maxwell-Yang-Mills equation. J. Differ. Geom.34, 275–345 (1991)
Graham, C. R., Lee, J. M.: Einstein metrics with prescribed conformal infinity on the ball. Adv. Math.87, 186–225 (1991)
Loewner, C., Nirenberg, L.: Partial differential equations invariant under conformal or projective transformations. In: Contributions to analysis. Ahlfors, L. V. et al. (eds.) New York: Academic Press 1974
Mazzeo, R.: Hodge cohomology of negatively curved manifolds. Technical report, 1986
Mazzeo, R.: The Hodge cohomology of conformally compact metrics. J. Differ. Geom.28, 309–339 (1988)
Mazzeo, R.: Regularity for the singular Yamabe problem. Stanford University preprint, 1990
Mazzeo, R., Melrose, R. B.: Meromorphic extension of the resolvent on complete spaces with asymptotically negative curvature. J. Funct. Anal.75, 260–310 (1987)
Melrose, R. B.: Transformation of boundary value problems. Acta Math.147, 149–236 (1981)
Penrose, R.: Zero rest-mass fields including gravitation: asymptotic behaviour. Proc. R. Soc. Lond.A284, 159–203 (1965)
Schoen, R. M.: Conformal deformation of a Riemannian metric to constant scalar curvature. J. Differ. Geom.20, 479–495 (1984)
Piotr T. Chruściel
Present address: Institute of Mathematics of the Polish Academy of Sciences, Warsaw
Department of Mathematics, Royal Institute of Technology, S-100 44, Stockholm, Sweden
Lars Andersson
Center for Mathematics and its Applications, Australian National University, T2601, Canberra, AC, Australia
Piotr T. Chruściel
Max-Planck Institut für Astrophysik, Karl-Schwarzschild-Strasse 1, W-8046, Garching bei München, FRG
Helmut Friedrich
Communicated by S.-T. Yau
Supported in part by NFR, the Swedish Academy of Sciences and the Gustavsson Foundation
About this article Cite this articleAndersson, L., Chruściel, P.T. & Friedrich, H. On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein's field equations. Commun.Math. Phys. 149, 587–612 (1992). https://doi.org/10.1007/BF02096944
Received: 03 May 1991
Revised: 24 April 1992
Issue Date: October 1992
DOI: https://doi.org/10.1007/BF02096944
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4