The Webster scalar curvature flow on CR sphere. Part II

TL;DR

This paper studies the Webster scalar curvature flow on the CR sphere to establish existence results for prescribing scalar curvature functions, utilizing Morse index assumptions to analyze the flow's behavior.

Contribution

It introduces a method using the Webster scalar curvature flow to prove existence of solutions under Morse index conditions, advancing the understanding of curvature prescription problems on CR spheres.

Findings

Existence of solutions under Morse index assumptions.

Application of the Webster scalar curvature flow to CR geometry.

Analysis of flow behavior leading to curvature prescription results.

Abstract

This is the second of two papers, in which we study the problem of prescribing Webster scalar curvature on the CR sphere as a given function f. Using the Webster scalar curvature flow, we prove an existence result under suitable assumptions on the Morse indices of f.