Helge Moller Pedersen:
Bilipschitz geometry of rational surface singularities.
<br><br>
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.