%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
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