Hyperbolic Geometry and the Helfrich Functional

Fuente: arXiv
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Main Authors: Palmer, Bennett, Pampano, Alvaro
Format: Preprint
Published: 2025
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author Palmer, Bennett
Pampano, Alvaro
author_facet Palmer, Bennett
Pampano, Alvaro
contents 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 ${\bf H}^3$. When the membrane surface meets the ideal boundary of hyperbolic space, a modification of the regularized area functional is related to the construction of closed equilibria for the Helfrich functional in ${\bf R}^3$.
format Preprint
id arxiv_https___arxiv_org_abs_2502_12434
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Hyperbolic Geometry and the Helfrich Functional
Palmer, Bennett
Pampano, Alvaro
Differential Geometry
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 ${\bf H}^3$. When the membrane surface meets the ideal boundary of hyperbolic space, a modification of the regularized area functional is related to the construction of closed equilibria for the Helfrich functional in ${\bf R}^3$.
title Hyperbolic Geometry and the Helfrich Functional
topic Differential Geometry
url https://arxiv.org/abs/2502.12434