On the Webster scalar curvature problem on the CR sphere with a cylindrical-type symmetry

TL;DR

This paper uses variational methods to construct multi-peak solutions for a Webster scalar curvature problem on the CR sphere with cylindrical symmetry, analyzing their asymptotic behavior as parameters vary.

Contribution

It introduces a novel variational approach to find multi-peak solutions in CR geometry with cylindrical symmetry, expanding understanding of scalar curvature problems.

Findings

Constructed multi-peak solutions under small parameter conditions

Analyzed asymptotic behavior of solutions

Demonstrated existence of solutions with cylindrical symmetry

Abstract

By variational methods, for a kind of Webster scalar curvature problems on the CR sphere with cylindrically symmetric curvature, we construct some multi-peak solutions as the parameter is sufficiently small under certain assumptions. We also obtain the asymptotic behaviors of the solutions.