Mathematics
Document Type
Article
Abstract
In this paper we study the problem of prescribing the Q ¯ ′ -curvature on embeddable pseudo-Einstein CR 3-manifolds. In the first stage we study the problem in the compact setting and we show that under natural assumptions, one can prescribe any positive (resp. negative) CR pluriharmonic function, if ∫ M Q ′ d v θ > 0 (resp. ∫ M Q ′ d v θ < 0 ). In the second stage, we study the problem in the non-compact setting of the Heisenberg group. Under mild assumptions on the prescribed function, we prove existence of a one parameter family of solutions. In fact, we show that one can find two kinds of solutions: normal ones that satisfy an isoperimetric inequality and non-normal ones that have a biharmonic leading term.
The available download on this page is the author manuscript accepted for publication. This version has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process.
Publication Title
Nonlinear Differential Equations and Applications
Publication Date
3-2023
Volume
30
Issue
2
ISSN
1021-9722
DOI
10.1007/s00030-023-00841-3
Keywords
32V05, 32V20, pseudo-Einstein manifolds, ∫ M Q ′ d v θ > 0 (resp. ∫ M Q ′ d v θ < 0, 82B05, statistical mechanics
Repository Citation
Maalaoui, Ali, "Prescribing the Q¯ ′ -curvature on pseudo-Einstein CR 3-manifolds" (2023). Mathematics. 2.
https://commons.clarku.edu/mathematics/2
Copyright
Published source must be acknowledged with citation: Maalaoui, A. (2023). Prescribing the Q¯′-curvature on pseudo-Einstein CR 3-manifolds. Nonlinear Differential Equations and Applications NoDEA, 30(2), 30. Must link to publisher version with DOI: https://doi.org/10.1007/s00030-023-00841-3