The generalized Poho{z}aev-Schoen identity and some geometric applications
Ezequiel Barbosa, Levi Lopes de Lima, Allan Freitas
TL;DR
This paper extends the Pohozaev-Schoen identity to derive new rigidity results for V-static manifolds and generalized solitons, and establishes an Alexandrov-type theorem for hypersurfaces in Einstein manifolds.
Contribution
It introduces a generalized Pohozaev-Schoen identity and applies it to obtain novel geometric rigidity and classification results.
Findings
Rigidity results for V-static manifolds and generalized solitons
An Alexandrov-type theorem for hypersurfaces in Einstein manifolds
Extension of Pohozaev-Schoen identity to new geometric contexts
Abstract
In this note we show how a generalized Pohozaev-Schoen identity due to Gover and Orsted \cite{GO} can be used to obtain some rigidity results for -static manifolds and generalized solitons. We also obtain an Alexandrov type result for certain hypersurfaces in Einstein manifolds.
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