Harmonic maps and associated energy functionals

Thesis

In this thesis, we study the existence and applications of harmonic maps in negative curvature settings. We cover three separate, but related strands of research.

Firstly, we study the existence of harmonic maps between complete simply connected negatively curved manifold. There have been many results in this vein, culminating in the result of Benoist–Hulin asserting the existence of a harmonic map at a finite distance from an arbitrary quasi-isometry between pinched Hadamar...

Expand abstract

Authors: Tošić, O

• DOI: 10.5287/ora-r8o8jo2om
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Teichmüller theory; energy functionals; mapping class groups; non-abelian Hodge theory; Higgs bundles; pinched Hadamard manifolds; harmonic maps
• Subjects: Geometric analysis; Differential geometry; Low-dimensional topology