TY - RPRT
T1 - The splitting theorem in non-smooth context
Y1 - 2013
A1 - Nicola Gigli
AB - 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.
UR - http://preprints.sissa.it/handle/1963/35306
U1 - 35613
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -