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Article Dans Une Revue Journal of Functional Analysis Année : 2023

The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant

Résumé

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.

Dates et versions

hal-03875566 , version 1 (28-11-2022)

Identifiants

Citer

Gilles Carron, Eric Chen, Yi Wang. The Yamabe flow on asymptotically Euclidean manifolds with nonpositive Yamabe constant. Journal of Functional Analysis, 2023, 284 (6), pp.109823. ⟨10.1016/j.jfa.2022.109823⟩. ⟨hal-03875566⟩
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