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MSRI-UP Colloquium: Tangents to Sigma-finite Curves July 10, 2015 (02:00 PM PDT - 03:30 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Bobby Wilson (University of Washington)
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In this talk, we will discuss the question of whether continuous, simple curves in Euclidean space with sigma-finite length have tangents at any points.  The results on $\sigma$-finite curves that we will discuss were initiated by the observation that the graph of a continuous function on [0,1] that satisfies a weak-Lipschitz property has sigma-finite one-dimensional Hausdorff measure. We will discuss our conclusion that every $\sigma$-finite curve has a tangent, in the pointwise sense, on a set of positive measure. This is joint work with M. Csornyei.

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