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Moduli Space of Anti-Self-Dual Poincaré-Einstein Metrics

par Ebrahimi, Mohammadamin
Président du jury Premoselli, Bruno
Promoteur Fine, Joel
Publication Non publié, 2025-10-06

Thèse de doctorat

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Résumé :

We show that, assuming a technical condition, the moduli space of anti-self-dual Poincaré–Einstein metrics is either empty or an immersed submanifold of the moduli space of Poincaré–Einstein metrics. Following Fine and Krasnov, we work in the definite connection formalism for Einstein and anti-self-duality equations.The analytic framework is provided by the Mazzeo–Melrose 0-calculus, used to study Fredholm properties of the relevant elliptic operators on asymptotically hyperbolic manifolds.