SELF-DUAL AND EVEN POINCARÉ-EINSTEIN METRICS IN DIMENSION FOUR

Journal of the Institute of Mathematics of Jussieu 2026 Open access

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Authors: Matthew J. Gursky, Stephen E. McKeown, Aaron J. Tyrrell
DOI: 10.1017/s1474748025101060
Cited by: 0
References: 19

Abstract

Abstract We prove rigidity and gap theorems for self-dual and even Poincaré-Einstein metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré-Einstein metrics in terms of conformal invariants of the boundary and the topology of the bulk. As a by-product of our proof, we identify a new scalar conformal invariant of three-dimensional Riemannian manifolds.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Geometry and complex manifolds Nonlinear Partial Differential Equations

Publication details

Journal / source
Journal of the Institute of Mathematics of Jussieu
Volume
25
Issue
2
Pages
749–779
Publication date
5 January 2026
Language
EN