Communications in Analysis and Geometry

Volume 28 (2020)

Number 2

The generalized Pohozaev-Schoen identity and some geometric applications

Pages: 223 – 242



Ezequiel Barbosa (Instituto de Ciências Exatas-Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil)

Allan Freitas (Departamento de Matemática, Universidade Federal da Paraíba, Brazil)

Levi Lopes de Lima (Departamento de Matemática, Universidade Federal do Ceará, Fortaleza, CE, Brazil)


In this note we show how a generalized Pohozaev–Schoen identity due to Gover and Orsted can be used to obtain some rigidity results for $V$-static manifolds and generalized solitons. We also obtain an Alexandrov type result for certain hypersurfaces in Einstein manifolds.

Received 5 April 2017

Accepted 23 October 2017

Published 6 May 2020