Curvature flows without singularities

• Applicant: Professor Dr. Oliver Schnürer
• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 336454636

We wish to investigate solutions to curvature flows like mean curvature flow. In particular, we want to study solutions that are given as proper graphs over time dependent domains. It turns out that not only the graphs above fulfil a curvature flow but in a weak sense also the boundaries of the domains below.We wish to investigate, whether there exist solutions with principal curvatures above bounded in terms of the geometry below and apply this to Neumann boundary conditions. We also want to give an existence proof for fully nonlinear curvature flows and find new graphical translating solutions to mean curvature flow.

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