Minimal Lagrangian connections and related structures

• Applicant: Professor Dr. Thomas Mettler
• Subject Area: Mathematics
• Term: since 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 339871296

Minimal Lagrangian connections and related structures are investigated. This includes a characterization of projective surfaces that are defined by a minimal Lagrangian connection, as well as an investigation of the related question of uniqueness of the relevant partial differential equation. Furthermore, possible relations to the Lagrangian mean curvature flow and short-time existence for a natural evolution equation for connections are analyzed. Relations to the theory of Anosov flows are also considered. In addition, Zoll projective structures on the 2-sphere are investigated.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2026: Geometry at Infinity
• International Connection: Switzerland