Numerical Finiteness Results for Minimal Surfaces in Three-Dimensional Space Forms

DOI10.1080/10586458.1997.10504618zbMath1115.53301OpenAlexW2014532681MaRDI QIDQ5756153

Ivo Nowak

Publication date: 16 August 2007

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1047047191

zbMATH Keywords

finite elementsvariational principleminimal surfacesfiniteness results

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Cites Work

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• Stationary minimal surfaces with boundary on a simplex
• On the Morse index of minimal surfaces in \({\mathbb{R}}^ p\) with polygonal boundaries
• Embedded minimal disks with a free boundary on a polyhedron in \({\mathbb R}^ 3\)
• Minimal surfaces with prescribed topological type on a Schwarzian chain in \(M^ 3_ c\)
• On the approximation of unstable parametric minimal surfaces
• Complete minimal surfaces in \(S^ 3\)
• A general existence theorem for surfaces of constant mean curvature
• Computing Discrete Minimal Surfaces and Their Conjugates
• Flow under Curvature: Singularity Formation, Minimal Surfaces, and Geodesics
• The Surface Evolver
• Minimizing the Squared Mean Curvature Integral for Surfaces in Space Forms

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