Geodesic metric spaces with unique blow-up almost everywhere: properties and examples

Mathematics – Metric Geometry

Scientific paper

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Oberwolfach report

Scientific paper

This short note has been written as an Oberwolfach report for the workshop "Differentialgeometrie im Grossen". We discuss properties of metric spaces that at almost all points admit a tangent metric space. We explain why, under some mild assumptions, the tangents are almost surely subFinsler Carnot groups. We mention several situations when the tangents are Euclidean spaces, but the initial metric spaces are quite pathological.

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