26 nov 2025 -- 10:00   [open in google calendar]

SNS, Sala Stemmi

Abstract.

The decomposability bundle of a Radon measure μ on R n, introduced by Alberti and Marchese, can be viewed as a kind of "tangent bundle" for measures. It describes the tangential directions associated with possible decompositions of μ into curves. The authors show that this bundle precisely characterizes the vector subspaces {v} for which vμ is a 1-dimensional flat chain.

In this work, we extend the discussion from curves to surfaces of arbitrary dimension k. We explore whether the previous characterization can be generalized to k-dimensional flat chains. Notably, the characterization does hold when k=n−1, but it fails for all intermediate dimensions.