@Article{ATA-40-57,
author = {Hogg , Joseph and Nguyen , Luc},
title = {Existence and Uniqueness for the Non-Compact Yamabe Problem of Negative Curvature Type},
journal = {Analysis in Theory and Applications},
year = {2024},
volume = {40},
number = {1},
pages = {57--91},
abstract = {<p style="text-align: justify;">We study existence and uniqueness results for the Yamabe problem on non-compact manifolds of negative curvature type. Our first existence and uniqueness
result concerns those such manifolds which are asymptotically locally hyperbolic. In
this context, our result requires only a partial $C^2$ decay of the metric, namely the full
decay of the metric in $C^1$ and the decay of the scalar curvature. In particular, no decay
of the Ricci curvature is assumed. In our second result we establish that a local volume
ratio condition, when combined with negativity of the scalar curvature at infinity, is
sufficient for existence of a solution. Our volume ratio condition appears tight. This
paper is based on the DPhil thesis of the first author.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2023-0014},
url = {http://global-sci.org/intro/article_detail/ata/23020.html}
}