Title: A Plateau Problem for Membranes

Author (Talk): Xinyi Liu, Northwestern University

Abstract:

We study fluid membranes with fixed area and bending resistance spanning two given closed curves, which may be non-planar and asymmetric. Using perturbation theory and numerical methods, we identify energy-minimizing shapes and introduce a tailored coordinate system to capture their complex geometries. These shapes generalize minimal surfaces like catenoids and can exhibit buckling and wrinkling. A direct correspondence in stability eigenvalues reveals a deep connection between minimal and elastic surfaces, offering insights into the forces and torques that stabilize cellular membranes and similar interfaces.