Variational structure of the $v_{\frac{n}{2}}$-Yamabe problem

TL;DR

This paper introduces a new variational framework and flow approach for the $v_{n/2}$-Yamabe problem, providing insights into solution uniqueness within conformal classes.

Contribution

It defines a novel Riemannian metric on conformal classes, leading to a new variational characterization and flow method for the $v_{n/2}$-Yamabe problem.

Findings

New variational characterization of the $v_{n/2}$-Yamabe problem

Introduction of a parabolic flow approach

Indication of solution uniqueness in conformal classes

Abstract

We define a new formal Riemannian metric on a conformal class in the context of the $v_{\frac{n}{2}}$-Yamabe problem. Our construction leads to a new variational characterization and a new parabolic flow approach to this problem. Moreover, this variational framework suggests that solutions to this problem are unique in a given conformal class.