On a new functional for extremal metrics of the conformal laplacian in high dimension

TL;DR

This paper introduces a new functional for the conformal spectrum of the conformal Laplacian on high-dimensional closed manifolds, providing a Korevaar type result and analyzing the sphere case with extensions to general manifolds.

Contribution

It presents a novel functional for the conformal spectrum of the conformal Laplacian and establishes a Korevaar type result, extending analysis to general closed manifolds.

Findings

New functional for conformal spectrum introduced

Korevaar type result established for the functional

Analysis extended from the sphere to general manifolds

Abstract

In this paper, we introduce a new functional for the conformal spectrum of the conformal laplacian on a closed manifold M of dimension at least 3. For this new functional we provide a Korevaar type result. The main body of the paper deals with the case of the sphere but a section is devoted to more general closed manifolds.