SELF-DUAL AND EVEN POINCARÉ-EINSTEIN METRICS IN DIMENSION FOUR
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.
Authors
- Aaron J. Tyrrell (ORCID: https://orcid.org/0000-0002-7314-2822)
- Matthew J. Gursky (ORCID: https://orcid.org/0000-0002-6868-3173)
- Stephen E. McKeown (ORCID: https://orcid.org/0000-0003-3036-0966)
Institutions
- University of Notre Dame (US)
- Texas Tech University (US)
- The University of Texas at Dallas (US)
Publication Details
- Journal
- Journal of the Institute of Mathematics of Jussieu
- Published
- 2026-01-05
- DOI
- https://doi.org/10.1017/s1474748025101060
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00