Mathematics

Title

Prescribing the Q¯ ′ -curvature on pseudo-Einstein CR 3-manifolds

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.

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

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