Non-compactness and infinite number of conformal initial data sets in high dimensions
Analysis of PDEs
2015-05-13 v1
Abstract
On any closed Riemannian manifold of dimension greater than , 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.
Keywords
Cite
@article{arxiv.1505.02806,
title = {Non-compactness and infinite number of conformal initial data sets in high dimensions},
author = {Bruno Premoselli and Juncheng Wei},
journal= {arXiv preprint arXiv:1505.02806},
year = {2015}
}