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arXiv · 2112.04207

Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary

Marco G. Ghimenti·Anna Maria Micheletti
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Abstract

We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum.

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Marco G. Ghimenti, Anna Maria Micheletti. 2021-12-08. Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary. https://arxiv.org/abs/2112.04207

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