English

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 77, 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}
}