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

2025/08/14 by Vaira, Giusi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10387

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≥ 8.

Citations

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• Blow-up phenomena for linearly perturbed Yamabe problem on manifolds\n with umbilic boundary
• Blowing up solutions for supercritical Yamabe problems on manifolds with umbilic boundary
• Positive Blow-up Solutions for a Linearly Perturbed Boundary Yamabe Problem
• Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with umbilic boundary
• Compactness and blow up results for doubly perturbed Yamabe problems on\n manifolds with non umbilic boundary