42 citations · 69 across the 13 of their papers we have counts for
5 papers · 1 filter
Examples of -unrectifiable normal currents
Andrea Schioppa
We construct new examples of normal (metric) currents using inverse systems of cube complexes. For any we provide examples of -dimensional normal currents whose associa…
The Lip-lip equality is stable under blow-up
Andrea Schioppa
We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an i…
PI spaces with analytic dimension 1 and arbitrary topological dimension
Bruce Kleiner, Andrea Schioppa
For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of Heinonen-Koskela, has topological dimension n, and has a measurab…
The Poincaré Inequality does not improve with blow-up
Andrea Schioppa
For each we construct a family of metric measure spaces which is closed under the operation of taking weak-tangents (i.e.~blow-ups), and such that each element of …
Infinitesimal structure of differentiability spaces, and metric differentiation
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa
We prove metric differentiation for differentiability spaces in the sense of Cheeger. As corollaries we give a new proof that the minimal generalized upper gradient coincides with…