Prescribed Webster Scalar Curvatures on Compact Pseudo-Hermitian Manifolds

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 c...

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Bibliographic Details
Published in:The Journal of geometric analysis 2022-05, Vol.32 (5), Article 151
Main Authors: Dong, Yuxin, Ren, Yibin, Yu, Weike
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Convex and Discrete Geometry
Deformation
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Manifolds
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Perturbation theory
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Summary: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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-00884-5