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arXiv · 2508.10387

Blow-up phenomena for a boundary Yamabe problem with umbilic boundary

Giusi Vaira
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Abstract

We consider a linear perturbation of the classical geometric problem of prescribing the scalar and the boundary mean curvature problem in a Riemannian manifold with umbilic boundary provided the Weyl tensor is non-zero everywhere. We will deal with the case of negative scalar curvature showing the existence of a positive solutions when $n\geq 8$.

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Giusi Vaira. 2025-08-14. Blow-up phenomena for a boundary Yamabe problem with umbilic boundary. https://arxiv.org/abs/2508.10387

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