Linear perturbation of the Yamabe problem on manifolds with boundary

TL;DR

This paper constructs blowing-up solutions for a linear perturbation of the 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 the perturbed Yamabe problem on manifolds with boundary when the dimension exceeds 6 and the boundary's second fundamental form is non-zero.

Findings

Successfully constructed blowing-up solutions under given conditions

Identified geometric criteria for solution behavior

Extended previous results to manifolds with boundary

Abstract

We build blowing-up solutions for linear 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.