On the relationship between derivations and measurable differentiable structures on metric measure spaces

2012/05/15 by Andrea Schioppa, Schioppa, Andrea
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.1205.3235

arxiv created 2012/05/15 · arxiv updated 2012/05/16

Abstract

We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module of derivations into free modules; [2] the existence of a measurable differentiable structure assuming that one can control the pointwise upper Lipschitz constant of a function through derivations; [3] an extension of a result of Keith about the choice of chart functions.

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