Hyperbolic Geometry and the Helfrich Functional
Abstract
Abstract 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 sessile and pendant drops in the hyperbolic space $$\textbf{H}^3$$ H 3 . When the membrane surface meets the ideal boundary of the hyperbolic space, a modification of the regularized area functional is related to the construction of closed equilibria for the Helfrich functional in $$\textbf{R}^3$$ R 3 .
Fields of Study & Subjects
Mathematics and Applications
History and Theory of Mathematics
Geometric and Algebraic Topology
Publication details
- Journal / source
- Journal of Geometric Analysis
- Volume
- 36
- Issue
- 8
- Publication date
- 7 July 2026
- Language
- EN