Schr{\"o}dinger maps to a K{\"a}hler manifold in two dimensions

TL;DR

This paper proves that Schr{"o}dinger maps into K{"a}hler manifolds are globally well-posed and scatter for small initial data in a Besov space, advancing understanding of their long-term behavior.

Contribution

It establishes the first global well-posedness and scattering results for Schr{"o}dinger maps into general K{"a}hler manifolds with small initial data.

Findings

Global well-posedness for small initial data

Scattering results for Schr{"o}dinger maps

Extension to general K{"a}hler manifolds

Abstract

We prove a global well--posedness and scattering result for Schr{\"o}dinger maps to a general K{\"a}hler manifold with small initial data in a Besov space.