Prescribed Webster scalar curvatures on compact pseudo-Hermitian manifolds

TL;DR

This paper studies how to prescribe Webster scalar curvatures on compact pseudo-Hermitian manifolds using methods like upper and lower solutions and perturbation theory, identifying functions realizable through CR conformal deformations.

Contribution

It introduces new criteria for realizing Webster scalar curvatures via CR conformal deformations on pseudo-Hermitian manifolds.

Findings

Characterization of curvature functions achievable through pointwise CR conformal deformations.

Identification of curvature functions realizable via CR conformally equivalent deformations.

Application of perturbation theory to analyze the prescribed curvature problem.

Abstract

In this paper, we investigate the problem of prescribing Webster scalar curvatures on compact pseudo-Hermitian manifolds. In terms of the method of upper and lower solutions and the perturbation theory of self-adjoint operators, we can describe some sets of Webster scalar curvature functions which can be realized through pointwise CR conformal deformations and CR conformally equivalent deformations respectively from a given pseudo-Hermitian structure.