Open Access
2008 On boundary value problems for Einstein metrics
Michael T Anderson
Geom. Topol. 12(4): 2009-2045 (2008). DOI: 10.2140/gt.2008.12.2009


On any given compact manifold Mn+1 with boundary M, it is proved that the moduli space of Einstein metrics on M, if non-empty, is a smooth, infinite dimensional Banach manifold, at least when π1(M,M)=0. Thus, the Einstein moduli space is unobstructed. The usual Dirichlet and Neumann boundary maps to data on M are smooth, but not Fredholm. Instead, one has natural mixed boundary-value problems which give Fredholm boundary maps.

These results also hold for manifolds with compact boundary which have a finite number of locally asymptotically flat ends, as well as for the Einstein equations coupled to many other fields.


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Michael T Anderson. "On boundary value problems for Einstein metrics." Geom. Topol. 12 (4) 2009 - 2045, 2008.


Received: 11 March 2008; Revised: 6 May 2008; Accepted: 9 June 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.58011
MathSciNet: MR2431014
Digital Object Identifier: 10.2140/gt.2008.12.2009

Primary: 58J05 , 58J32
Secondary: 53C25

Keywords: Einstein metrics , elliptic boundary , value problems

Rights: Copyright © 2008 Mathematical Sciences Publishers

Vol.12 • No. 4 • 2008
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