3 papers
math.DG2025
Hyperbolic Geometry and the Helfrich Functional
Bennett Palmer, Alvaro Pampano
The Helfrich model is a fundamental tool for determining the morphology of biological membranes. We relate the geometry of an important class of its equilibria to the geometry of s…
math.DG2025
Axially Symmetric Helfrich Spheres
Rafael López, Bennett Palmer, Álvaro Pámpano
Smooth axially symmetric Helfrich topological spheres are either round or else they must satisfy a second order equation known as the reduced membrane equation [17]. In this paper,…
math.DG2024
Stability of Membranes
Bennett Palmer, Alvaro Pampano
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this…