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Local structure theory of Einstein manifolds with boundary

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arxiv 2405.17577 v1 pith:H46AGFZI submitted 2024-05-27 math.DG gr-qc

Zhongshan An , Lan-Hsuan Huang This is my paper · ORCID
classification math.DGgr-qc
keywords boundaryeinsteinmetricslocalstructurethreeandersoncompact
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We study local structure of the moduli space of compact Einstein metrics with respect to the boundary conformal metric and mean curvature. In dimension three, we confirm M. Anderson's conjecture in a strong sense, showing that the map from Einstein metrics to such boundary data is generically a local diffeomorphism. In dimensions greater than three, we obtain similar results for Ricci flat metrics and negative Einstein metrics under new non-degenerate boundary conditions.

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Cited by 4 Pith papers

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