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- On the Differential Structure of Metric Measure Spaces and Applications
On the Differential Structure of Metric Measure Spaces and Applications
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The main goals of this paper are to develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions, to employ these notions of calculus to provide a general definition of distributional Laplacian, and to show that on spaces with Ricci curvature bounded from below and dimension bounded from above, the Laplacian of the distance function is always a measure and that this measure has the standard sharp comparison properties.
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