A perturbation approach for Paneitz energy on standard three sphere

TL;DR

This paper offers a new proof of the sharp Paneitz inequality on the three sphere using a perturbation approach and introduces a novel symmetrization technique for higher order variational problems.

Contribution

It provides a new proof method for the Paneitz inequality and introduces a symmetrization process applicable to higher order variational problems.

Findings

New proof of the sharp Paneitz inequality on the three sphere

Development of a symmetrization technique for extremal functions

Application of subcritical approximation in higher order problems

Abstract

We present another proof of the sharp inequality for Paneitz operator on the standard three sphere, in the spirit of subcritical approximation for the classical Yamabe problem. To solve the perturbed problem, we use a symmetrization process which only works for extremal functions. This gives a new example of symmetrization for higher order variational problems.