On Open Scattering Channels for a Branched Covering of the Euclidean Plane

TL;DR

This paper investigates the openness of scattering channels in a geometric model involving a double covering of the Euclidean plane with branch points, demonstrating stability under metric perturbations.

Contribution

It proves that scattering channels are open in this model and that this property remains stable under certain metric perturbations.

Findings

Scattering channels are open in the studied geometric model.

Openness of channels is stable under metric perturbations.

The model involves a double covering of the plane with branch points.

Abstract

We study the interaction of two scattering channels for a simple geometric model consisting in a double covering of the plane with two branch points, equipped with the Euclidean metric. We show that the scattering channels are open in the sense of arXiv:1202.0333 and that this property is stable under suitable perturbations of the metric.