<p>In this brief note, we deal with Serrin-type problems on Riemannian manifolds. Firstly, we provide a Soap Bubble-type theorem and rigidity results. In another direction, we obtain a rigidity result addressed to annular regions in Einstein manifolds endowed with a conformal vector field.</p>

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Rigidity of Serrin-Type Problems via Integral Identities

  • J. de Lima,
  • M. S. Santos,
  • J. S. Sindeaux

摘要

In this brief note, we deal with Serrin-type problems on Riemannian manifolds. Firstly, we provide a Soap Bubble-type theorem and rigidity results. In another direction, we obtain a rigidity result addressed to annular regions in Einstein manifolds endowed with a conformal vector field.