Calculus of Variations and Geometric Measure Theory
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N. Gigli

The splitting theorem in non-smooth context

created by gigli on 28 Jan 2013
modified on 22 Feb 2013


Submitted Paper

Inserted: 28 jan 2013
Last Updated: 22 feb 2013

Year: 2013


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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