%0 Report %D 2013 %T The splitting theorem in non-smooth context %A Nicola Gigli %X 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. %G en %U http://preprints.sissa.it/handle/1963/35306 %1 35613 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2018-02-23T12:45:43Z No. of bitstreams: 1 Splittingmms-submitted.pdf: 826242 bytes, checksum: 0395e29f7f4d768880e012ef1a77073a (MD5)