Lipschitz geometry of complex plane algebraic curves.

Abstract

We present the complete classification of complex plane algebraic curves, equipped with the induced Euclidean metric, up to global bilipschitz homeomorphism. In particular, we prove a theorem giving a complete classification of the Lipschitz geometry at infinity of complex algebraic plane curves. We synthesize combinatorial objects that encode both Lipschitz geometry and Lipschitz geometry at infinity of complex algebraic plane curves.