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

TL;DR

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

Contribution

It introduces a method to build blowing-up solutions for supercritical Yamabe problems on manifolds with non-umbilic boundary, considering dimensions greater than 6.

Findings

Successfully constructed blowing-up solutions under given conditions

Identified geometric conditions necessary for solution blow-up

Extended previous results to supercritical regimes

Abstract

We build blowing-up solutions for a supercritical perturbation of the Yamabe problem on manifolds with boundary, provided the dimension of the manifold is n>6 and the trace-free part of the second fundamental form is non-zero everywhere on the boundary.