The complex landslide flow and the method of integrable systems

TL;DR

This paper explores the relationship between complex landslide flows on Teichmüller spaces and integrable systems, showing how holonomy can be derived from harmonic maps into hyperbolic space.

Contribution

It establishes a novel connection between complex landslide flows and integrable systems via harmonic maps and flat connections.

Findings

Holonomy of complex landslide flow derived from harmonic maps.

Connection between Teichmüller spaces and integrable systems.

Framework for analyzing landslide flows using flat connections.

Abstract

We investigate a connection between the complex landslide flow, defined on a pair of Teichm\"uller spaces, and the integrable system approach to harmonic maps into a symmetric space. We will prove that the holonomy of the complex landslide flow can be derived from the holonomy of the family of flat connections determined by a harmonic map into the hyperbolic two-space.