Differentiability of Lipschitz functions inside thin sets

Olga Maleva (Birmingham)

Wednesday 18th November, 2009 15:00-16:00 326


A theorem of Lebesgue says that a subset of the real line has measure 0 if and only if some Lipschitz function is not differentiable anywhere in this set. But in higher dimensions, whilst the "if" part is still true, there exist exceptional sets of measure 0 such that every Lipschitz function is differentiable on a dense subset of the set. I will show that such sets can even be compact and of Hausdorff dimension 1. I will also discuss how this may lead to a solution of a long-standing open problem in geometric measure theory.

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