Equivariant Yamabe problem and Hebey-Vaugon conjecture

TL;DR

This paper advances the understanding of the Yamabe problem with symmetry by proving the Hebey-Vaugon conjecture in new cases, extending Aubin's theorem and contributing to geometric analysis.

Contribution

The paper generalizes Aubin's theorem and proves the Hebey-Vaugon conjecture in additional cases, expanding the scope of solutions to the Yamabe problem with symmetry.

Findings

Proved the Hebey-Vaugon conjecture in new cases

Extended Aubin's theorem to broader contexts

Enhanced understanding of the Yamabe problem with isometry groups

Abstract

In their study of the Yamabe problem in the presence of isometry group, Hebey and Vaugon announced a conjecture. This conjecture generalizes Aubin's conjecture, which has already been proven and is sufficient to solve the Yamabe problem. In this paper, we generalize Aubin's theorem and we prove the Hebey--Vaugon conjecture in some new cases.