Metric spaces with dilations, and metric trees

Here is a gentle introduction to the theory of metric spaces with dilations ("rescaling maps", so that one can define an appropriate notion of tangent space.) This appears on the arXiv today.

http://arxiv.org/abs/1007.2362

Also a couple of elegant-looking papers on metric trees and their embeddings into Banach spaces

http://arxiv.org/abs/1007.2207

http://arxiv.org/abs/1007.2208

Lots of interesting stuff on the arXiv today. I probably won't be posting much for a few weeks as I have some personal business to take care of.