Blowing up solutions for supercritical Yamabe problems on manifolds with umbilic boundary

TL;DR

This paper constructs blowing-up solutions for a supercritical Yamabe problem on manifolds with umbilic boundary, under specific geometric conditions, advancing understanding of geometric PDEs in high dimensions.

Contribution

It introduces new blowing-up solutions for the supercritical Yamabe problem on manifolds with umbilic boundary when the dimension exceeds 7 and the Weyl tensor is non-zero on the boundary.

Findings

Existence of blowing-up solutions under specified conditions

Solutions depend on the non-vanishing of the Weyl tensor on the boundary

Results apply to manifolds with dimension greater than 7

Abstract

We build blowing-up solutions for a supercritical perturbation of the Yamabe problem on manifolds with umbilic boundary provided the dimension of the manifold is n>7 and that the Weyl tensor W(x) is not vanishing on the boundary of M.