On the essential minimal volume of Einstein 4-manifolds

Volume minimal essentiel des 4 dimensions d'Einstein

Antoine Song (1) , Fanny Bastien (2) , Hugo Béchet (2)

1 UC Berkeley - University of California [Berkeley]
2 IF - Institut Fourier

Summer School 2021. Given a positive epsilon, a closed Einstein 4-manifold admits a natural thick-thin decomposition. I will explain how, for any delta, one can modify the Einstein metric to a bounded sectional curvature metric so that the thick part has volume linearly bounded by the Euler characteristic and the thin part has injectivity radius less than delta. I will also discuss relations to conjectural obstructions to collapsing with bounded sectional curvature or to the existence of Einstein metrics.

Mots clés: eem2021; grenoble; curvature constraints and spaces of metrics; minimal volume; Einstein 4-manifolds; eem2021

Mots clés: contraintes de courbures et espaces métriques; contraintes de courbures et espaces métriques

Domaines: Mathématiques [math]

Antoine Song, Fanny Bastien, Hugo Béchet. On the essential minimal volume of Einstein 4-manifolds: Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03677272⟩