## On Curvature-Dimension Condition and Bochners Inequality for Metric Measure Spaces

#### Karl SturmUniversität Bonn

Equipped with the L^2-distortion distance, the space "X" of all metric measure spaces (X,d,m) is proven to have nonnegative curvature in the sense of Alexandrov. Geodesics and tangent spaces are characterized in detail. Moreover, classes of semiconvex functionals and their gradient flows on "X" are presented.

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