Analysis of Multi-phase Membranes

Biological membranes are key to cellular function, but their mathematical modeling remains a major challenge—especially when accounting for multiple materials rather than homogeneous structures. While past research (including breakthroughs like the Willmore conjecture) has advanced our understanding of uniform membranes, structured membranes demand deeper analytical exploration. This project investigates membranes composed of different materials, modeling their evolution via the Canham-Helfrich functional with varying material parameters and interfacial elastic effects.

Our goal is to establish rigorous analytical results—examining solution existence, stability, and singularity formation—for these highly complex, coupled quasilinear systems. Combining geometric analysis with insights from numerical studies, we aim to push theoretical boundaries and uncover new dynamical behaviors in membrane physics. Funded by the Austrian Science Fund (FWF), this work expands the frontiers of mathematical biology and geometric PDEs.