The splitting theorem in non-smooth context

Nicola Gigli (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

We prove that an infinitesimally Hilbertian CD(0,N) space containing a line splits as the product of $R$ and an infinitesimally Hilbertian CD(0,N-1) space. By 'infinitesimally Hilbertian' we mean that the Sobolev space $W^{1,2}(X,d,m)$, which in general is a Banach space, is an Hilbert space. When coupled with a curvature-dimension bound, this condition is known to be stable with respect to measured Gromov-Hausdorff convergence.

Domains: Metric Geometry [math.MG]; Differential Geometry [math.DG]

Nicola Gigli. The splitting theorem in non-smooth context. 2013. ⟨hal-00920386⟩