Submitted Paper
Inserted: 28 jan 2013
Last Updated: 22 feb 2013
Year: 2013
Abstract:
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
Keywords: Metric Geometry
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