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arXiv · 1505.02806

Non-compactness and infinite number of conformal initial data sets in high dimensions

Bruno Premoselli·Juncheng Wei
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Abstract

On any closed Riemannian manifold of dimension greater than $7$, we construct examples of background physical coefficients for which the Einstein-Lichnerowicz equation possesses a non-compact set of positive solutions. This yields in particular the existence of an infinite number of positive solutions in such cases.

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Bruno Premoselli, Juncheng Wei. 2015-05-11. Non-compactness and infinite number of conformal initial data sets in high dimensions. https://arxiv.org/abs/1505.02806

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