A Simpler Proof of Frank and Lieb's Sharp Inequality on the Heisenberg Group

TL;DR

This paper presents a simplified proof of the sharp Frank-Lieb inequality on the Heisenberg group, avoiding complex existence arguments by analyzing second variations of subcritical functionals.

Contribution

It introduces a more straightforward proof method for the Frank-Lieb inequality on the Heisenberg group, enhancing understanding and accessibility.

Findings

Proof simplifies the original argument for the inequality

Avoids the need for complex minimizer existence proofs

Provides insights into second variation techniques

Abstract

We give a simpler proof of the sharp Frank-Lieb inequality on the Heisenberg group. The proof bypasses the sophisticated argument for existence of a minimizer and is based on the study of the 2nd variation of subcritical functionals using their fundamental techniques.