| Résume | Lipschitz geometry is a branch of singularity theory that studies the metric data of a germ of a complex analytic space.
I will discuss a new approach to the study of such metric germs, and in particular of an invariant called Lipschitz inner rate, based on the combinatorics of a space of valuations, the so-called non-archimedean link of the singularity. I will describe completely the inner metric structure of a complex surface germ showing that its inner rates both determine and are determined by global geometric data: the topology of the germ, its hyperplane sections, and its generic polar curves.
This is a joint work with André Belotto and Anne Pichon.
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