A Björling representation for Jacobi fields on minimal surfaces and soap film instabilities
DOI10.1098/rspa.2019.0903zbMath1472.53066arXiv1912.13009OpenAlexW3102758653WikidataQ98649509 ScholiaQ98649509MaRDI QIDQ5160975
Thomas Machon, Gareth P. Alexander
Publication date: 29 October 2021
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.13009
geometryminimal surfaceinstabilitiesmathematical physicsapplied mathematicssoap filmBjörling representation
Thin fluid films (76A20) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)
Cites Work
- Unnamed Item
- Unnamed Item
- Stability of minimal surfaces and eigenvalues of the Laplacian
- Explicit Björling surfaces with prescribed geometry
- Soap films with gravity and almost-minimal surfaces
- One-sided complete stable minimal surfaces
- Bending the helicoid
- Complete minimal Möbius strips in \(\mathbb R^n\) and the Björling problem
- Minimal varieties in Riemannian manifolds
- Boundary singularities produced by the motion of soap films
- The classical theory of minimal surfaces
- Topological constraints and their breakdown in dynamical evolution
- A cubic structure consisting of a lipid bilayer forming an infinite periodic minimum surface of the gyroid type in the glycerolmonooleat-water system
- The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
- Stable complete minimal surfaces in 𝑅³ are planes
- On the Size of a Stable Minimal Surface in R 3
- Dynamics of inviscid capillary breakup: collapse and pinchoff of a film bridge
- Soap-film Möbius strip changes topology with a twist singularity
- Minimal surfaces bounded by elastic lines
- Soap Film Experiments with Minimal Surfaces
