A relation between cylindrical critical points of Willmore-type energies, weighted areas and vertical potential energies

DOI10.1016/j.geomphys.2022.104731OpenAlexW4312038440WikidataQ125261469 ScholiaQ125261469MaRDI QIDQ2684761

Publication date: 17 February 2023

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.01070

zbMATH Keywords

stability elastic curve Willmore hypersurface weighted area singular minimal hypersurface stationary hypersurface

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Nonlinear elliptic equations (35J60) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items (1)

Generalized elastic translating solitons

Cites Work

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Planar \textit{p}-elastic curves and related generalized complete elliptic integrals
Flow by mean curvature of convex surfaces into spheres
The $n$-dimensional analogue of the catenary: Existence and non-existence
The stability of the axially symmetric pendent drop
The two-dimensional analogue of the catenary
The conformal Gauss map and the stability of Willmore surfaces
Isoperimetry of waists and concentration of maps
Constant mean curvature invariant surfaces and extremals of curvature energies
Generalized elastica problems under area constraint
Stationary soap films with vertical potentials
Plateau-Rayleigh instability of singular minimal surfaces
A dome subjected to compression forces: a comparison study between the mathematical model, the catenary rotation surface and the paraboloid
Stability of stationary points for one-dimensional Willmore energy with spatially heterogeneous term
The Euler-Helfrich functional
Classification of rotational surfaces with constant skew curvature in 3-space forms
A gradient flow for the $p$-elastic energy defined on closed planar curves
Total $p$-powered curvature of closed curves and flat-core closed $p$-curves in $S^2(G)$
On the stability of the CMC Clifford tori as constrained Willmore surfaces
The one dimensional case of the singular minimal surfaces with density
On the variation of curvature functionals in a space form with application to a generalized Willmore energy
Min-max theory and the Willmore conjecture
A varifold perspective on the $p$-elastic energy of planar sets
Capillary channels in a gravitational field
Area-Minimizing Surfaces, Faces of Grassmannians, and Calibrations
The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
Elliptic regularization and partial regularity for motion by mean curvature
A geometric theory on the elasticity of bio-membranes
Geometry and stability of bubbles with gravity
Classification of rotational surfaces in Euclidean space satisfying a linear relation between their principal curvatures
A Second Order Gradient Flow of p-Elastic Planar Networks

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