Non-compactness and infinite number of conformal initial data sets in high dimensions
classification
🧮 math.AP
keywords
infinitenumberpositivesolutionsbackgroundcasesclosedcoefficients
read the original 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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