Sharp Stability of Global Compactness on the Heisenberg Group

TL;DR

This paper proves a precise stability inequality on the Heisenberg group, showing that functions near a sum of specific bubbles exhibit stable behavior, leading to a quantitative understanding of compactness.

Contribution

It introduces a sharp stability inequality for functions close to Jerison-Lee bubbles on the Heisenberg group, advancing the understanding of global compactness stability.

Findings

Established a sharp stability inequality on the Heisenberg group.

Achieved a quantitative stability result for global compactness.

Demonstrated stability for functions near Jerison-Lee bubbles.

Abstract

In this paper, we establish a sharp stability inequality on the Heisenberg group for functions that are close to the sum of m weakly interacting Jerison-Lee bubbles. As a consequence, we obtain a sharp quantitative stability of global compactness for non-negative functions on Heisenberg group.