The Initial Value Problem for Harmonic maps of Cohomogeneity One manifolds

TL;DR

This paper establishes the local existence of equivariant harmonic maps of cohomogeneity one manifolds near singular orbits and develops related theory for regular-singular systems.

Contribution

It introduces a method to solve the initial value problem for harmonic maps in cohomogeneity one settings, including singular orbit analysis.

Findings

Proved local existence of harmonic maps near singular orbits.

Developed theory for regular-singular first order systems.

Extended harmonic map theory to cohomogeneity one manifolds.

Abstract

We set up and solve the initial value problem for equivariant harmonic maps of cohomogeneity one manifolds, i.e. we show the local existence of a harmonic map in the neighborhood of a singular orbit. Furthermore, we present some theory of regular-singular systems of first order.