Differentiability and Directional Differentiability in Laakso Spaces

Abstract

In recent years many aspects of first order calculus have been extended to metric measure spaces which are doubling and support a Poincare inequality. Laakso spaces were constructed by Laakso to show that such spaces can have any dimension Q>1. We introduce Laakso space and describe recent work investigating the relationship between existence of a maximal directional derivative and differentiability. In particular, the connection with differentiability of the distance described in the first talk breaks down in this setting. Joint work with Capolli and Pinamonti.

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