Prescribed Ricci curvature near an Einstein manifold with boundary
Differential Geometry
2025-03-25 v1
Abstract
Let (M, g) be a compact Einstein Riemannian manifold with boundary. We show that under certain conditions, the map that associates to a metric on M its Ricci curvature, its induced conformal class on the boundary, and its mean curvature on the boundary is locally invertible near g. The contravariant Ricci operator, as well as other operators such as the Einstein operator, are also studied.
Keywords
Cite
@article{arxiv.2503.18452,
title = {Prescribed Ricci curvature near an Einstein manifold with boundary},
author = {Erwann Delay},
journal= {arXiv preprint arXiv:2503.18452},
year = {2025}
}