Geometric evolution equations of fourth order

• Applicant: Professorin Dr. Elena Mäder-Baumdicker
• Subject Area: Mathematics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 575403317

Many natural objects can be described as surfaces or interfaces that evolve to minimize energy. This evolution is often influenced by the curvature of the surface, leading to complex mathematical equations known as fourth-order geometric evolution equations. These equations are difficult to analyze because standard techniques do not work well with them. This project aims to help bridge that gap by developing new mathematical tools to better understand these equations. In particular, the researchers will focus on differentiable Harnack inequalities and the Willmore flow. The latter is used to learn more about the topological structure of spherical immersions. The approach involves new techniques, including novel entropy-based methods, analysis of the bi-heat kernel, and topological tools related to the multiplicity of self-intersections of surfaces.

• DFG Programme: Research Grants