Helge Moller Pedersen:
Bilipschitz geometry of rational surface singularities.
Abstract: Let $(X,0)\subset(\mathbbm{C}^N,0)$ be a germ of complex
singularity. The hermitian metric of $\mathbbm{C}^N$ induces two metrics
on $(X,0)$ called the outer and the inner metric. The bilipschitz type
of these metrics is independent of the choice of embedding. It is well
known that the topology of $(X,0)$ is a cone over the link. A natural
question is then when is the inner (or outer) metric bilipschitz
equivalent to a metric cone? We will give a complete answer to this
question when $(X,0)$ is a rational surface singularity, using the
thick-thin decomposition of Birbrair, Neumann and Pichon. We will then
restrict ourselves to minimal singularities, and describe the complete
classification of their inner (and outer) metric, and especially show
that it is determined by the topology.