Accepted Paper
Inserted: 5 aug 2022
Last Updated: 26 mar 2024
Journal: Communications in Contemporary Mathematics
Year: 2022
Abstract:
We investigate the connection between maximal directional derivatives and differentiability for Lipschitz functions defined on Laakso space. We show that maximality of a directional derivative for a Lipschitz function implies differentiability only for a $\sigma$-porous set of points. On the other hand, the distance to a fixed point is differentiable everywhere except for a $\sigma$-porous set of points. This behavior is very different to the previously studied settings of Euclidean spaces and Carnot groups.
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