New developments on the p-Willmore energy of surfaces

DOI10.7546/giq-21-2020-57-65zbMath1483.53079OpenAlexW3091794314MaRDI QIDQ1980255

Anthony Gruber, Eugenio Aulisa, Hung Tran, Magdalena Daniela Toda

Publication date: 3 September 2021

Full work available at URL: https://doi.org/10.7546/giq-21-2020-57-65

zbMATH Keywords

minimal surfacesWillmore energyWillmore flowcurvature functionals

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Geometric evolution equations (53E99)

Uses Software

• GitHub

Cites Work

• The Willmore conjecture
• A duality theorem for Willmore surfaces
• Extremals of the generalized Euler-Bernoulli energy and applications
• Index characterization for free boundary minimal surfaces
• The many faces of elastica
• The Willmore boundary problem
• On the variation of curvature functionals in a space form with application to a generalized Willmore energy
• Error analysis of a finite element method for the Willmore flow of graphs
• Variational problems of minimal surface type. II: Boundary value problems for the minimal surface equation
• Boundary value problems for the one-dimensional Willmore equation
• A geometric theory on the elasticity of bio-membranes
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