Mathematics
functional determinant on pseudo-einstein 3-manifolds
Document Type
Article
Abstract
Given a three-dimensional pseudo-Einstein CR manifold (M, T1,0M, θ), we establish an expression for the difference of determinants of the Paneitz type operators Aθ, related to the problem of prescribing the Q′-curvature, under the conformal change θ → ewθ with (Formula presented) the space of pluriharmonic functions. This generalizes the expression of the functional determinant in four-dimensional Riemannian manifolds established in (Proc. Amer. Math. Soc. 113:3 (1991), 669–682). We also provide an existence result of maximizers for the scaling invariant functional determinant as in (Ann. of Math. (2) 142:1 (1995), 171–212).
Publication Title
Pacific Journal of Mathematics
Publication Date
2020
Volume
309
Issue
2
First Page
421
Last Page
436
ISSN
0030-8730
DOI
10.2140/pjm.2020.309.421
Keywords
functional determinant, pseudo-Einstein CR manifolds, the P′-operator
Repository Citation
Maalaoui, Ali, "functional determinant on pseudo-einstein 3-manifolds" (2020). Mathematics. 20.
https://commons.clarku.edu/mathematics/20
