Pseudoholomorphic simple Harnack curves

TL;DR

This paper provides a new proof of Mikhalkin's theorem, extending the topological classification of simple Harnack curves to include real pseudoholomorphic curves, thereby broadening the understanding of their geometric properties.

Contribution

The authors present a novel proof that generalizes Mikhalkin's classification to encompass real pseudoholomorphic curves, enhancing the theoretical framework.

Findings

Extended classification to pseudoholomorphic curves

Provided a new proof of Mikhalkin's theorem

Broadened understanding of Harnack curves

Abstract

We give a new proof of Mikhalkin's Theorem on the topological classification of simple Harnack curves, which in particular extends Mikhalkin's result to real pseudoholomorphic curves.