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arXiv · 2207.07003

The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant

Gilles Carron·Eric Chen·Yi Wang
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Abstract

We study the Yamabe flow on asymptotically flat manifolds with non-positive Yamabe constant $Y\leq 0$. Previous work by the second and third named authors \cite{ChenWang} showed that while the Yamabe flow always converges in a global weighted sense when $Y>0$, the flow must diverge when $Y\leq 0$. We show here in the $Y\leq 0$ case however that after suitable rescalings, the Yamabe flow starting from any asymptotically flat manifold must converge to the unique positive function which solves the Yamabe problem on a compactification of the original manifold.

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Gilles Carron, Eric Chen, Yi Wang. 2022-07-14. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant. https://arxiv.org/abs/2207.07003

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