Membrane Mechanics Meet Minimal Manifolds

When

February 13, 2023 | 3:30 p.m. - 4:30 p.m.
Refreshments at 3:00 in Lobby

Where

University Hall 1005

Speaker

Leroy Jia

Abstract

A time-honored problem in mathematical physics is to show that an area-minimizing fluid interface such as a soap film forms a special surface whose mean curvature vanishes. In the axisymmetric setting, this surface is called a catenoid. We recap Euler's original solution to the catenoid problem and then proceed to discuss a generalization of this problem where the fluid interface is replaced by a membrane with a bending stiffness. The shapes that such a membrane can make, which are critical surfaces of an energy called the Willmore functional, are intimately related to the catenoid and also to the shapes of a compressed rod (i.e., the elastica) in a precise mathematical way that informs us about their mechanics.