France-Italy meeting in Geometric Analysis

Stability of lower curvature bounds under $C^0$ deformations of the metric

speaker: Thomas Richard (Université Paris Est Créteil)

abstract: If a sequence of Riemannian manifolds with sectional curvature bounded from below Gromov-Hausdorff converges to a smooth limit manifold, then the limit has sectional curvature bounded from below. This comes from the fact that lower bounds on the sectional curvature have a strong geometric meaning in term of « fatness of geodesic triangles » through Toponogov’s theorem. The aim of this talk is to show how one can deal with other kind of curvature bounds which do not have such a strong geometric flavor (like lower bounds on the curvature operator), at the cost of requiring $C^0$ convergence of the metric instead of Gromov-Hausdorff convergence. This builds up on previous works by Koch-Lamm and Bamler.

timetable:
Wed 22 Feb, 10:30 - 11:30, Aula Dini
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