Stratified spaces and synthetic Ricci curvature bounds

Ilaria Mondello (1) , J. Bertrand (2) , C Ketterer , T. Richard (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove that a compact stratied space satises the Riemannian curvature-dimension condition RCD(K, N) if and only if its Ricci tensor is bounded below by K ∈ R on the regular set, the cone angle along the stratum of codimension two is smaller than or equal to 2π and its dimension is at most equal to N. This gives a new wide class of geometric examples of metric measure spaces satisfying the RCD(K, N) curvature-dimension condition, including for instance spherical suspensions, orbifolds, Kähler-Einstein manifolds with a divisor, Einstein manifolds with conical singularities along a curve. We also obtain new analytic and geometric results on stratied spaces, such as Bishop-Gromov volume inequality, Laplacian comparison, Lévy-Gromov isoperimetric inequality.

Domaines: Géométrie différentielle [math.DG]

Ilaria Mondello, J. Bertrand, C Ketterer, T. Richard. Stratified spaces and synthetic Ricci curvature bounds . 2018. ⟨hal-01773881v2⟩