On the Evolution of Regularized Dirac-Harmonic Maps from Closed Surfaces

2014/06/30 by Volker Branding
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Convergence (economics) #Dirac (video compression format) #Evolution equation #Geometric Analysis and Curvature Flows #Gravitational singularity #Harmonic #Harmonic map #Mathematical analysis #Mathematics #Numerical methods in inverse problems #Physics #Pure mathematics #Quantum mechanics #Regularization (linguistics) #math-ph #math.AP #math.DG #math.MP #msc:53C27 #msc:53C43 #msc:58E20 #msc:58J35

paper · pdf · doi:10.1007/s00025-020-1178-5

published as Results in Mathematics, Volume 75, Article number: 57 (2020)

openalex publication_date 2020/03/18 · arxiv created 2020/07/03 · arxiv updated 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We study the evolution equations for a regularized version of Dirac-harmonic maps from closed Riemannian surfaces. We establish the existence of a global weak solution for the regularized problem, which is smooth away from finitely many singularities. Moreover, we discuss the convergence of the evolution equations and address the question if we can remove the regularization in the end.

Citations

• Dirac-harmonic maps
• Liouville theorems for Dirac-harmonic maps
• On the evolution of harmonic mappings of Riemannian surfaces
• The Existence of Minimal Immersions of 2-Spheres
• The Analysis of Harmonic Maps and their Heat Flows