Integral iterations for harmonic maps

2017/04/05 by Andrew Neitzke, Neitzke, Andrew · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Differential Equations Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1704.01522

openalex publication_date 2017/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study minimal harmonic maps g: ℂ → SO(3) \backslash SL(3,ℝ), parameterized by polynomial cubic differentials P in the plane. The asymptotic structure of such a g is determined by a convex polygon Y(P) in \mathbbRP². We give a conjectural method for determining Y(P) by solving a fixed-point problem for a certain integral operator. The technology of spectral networks and BPS state counts is a key input to the formulation of this fixed-point problem. We work out two families of examples in detail.

Cited by

• Spectral networks for polynomial cubic differentials

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