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Compactness results for linearly perturbed Yamabe problem on manifolds with boundary

  • * Corresponding author: Marco Ghimenti

    * Corresponding author: Marco Ghimenti 
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  • Let $ (M,g) $ a compact Riemannian $ n $-dimensional manifold. It is well know that, under certain hypothesis, in the conformal class of $ g $ there are scalar-flat metrics that have $ \partial M $ as a constant mean curvature hypersurface. Also, under certain hypothesis, it is known that these metrics are a compact set. In this paper we prove that, both in the case of umbilic and non-umbilic boundary, if we linearly perturb the mean curvature term $ h_{g} $ with a negative smooth function $ \alpha, $ the set of solutions of Yamabe problem is still a compact set.

    Mathematics Subject Classification: 35J65, 53C21.


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