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arXiv · 1912.11482

Compactness results for linearly perturbed Yamabe problem on manifolds with boundary

Marco Ghimenti·Anna Maria Micheletti
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Abstract

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 the boundary of 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 with a negative smooth function, the set of solutions of Yamabe problem is still a compact set.

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Marco Ghimenti, Anna Maria Micheletti. 2019-12-24. Compactness results for linearly perturbed Yamabe problem on manifolds with boundary. https://arxiv.org/abs/1912.11482

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