Geodesic
On axisymmetric Helfrich surfaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 854-861

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In this paper we study axisymmetric Helfrich surfaces. We prove the convergence of the formal power series solution of the Euler–Lagrange equation for the Helfrich functional in a neighborhood of its singular point. We also prove the following inequality $$ \lambda_v R^3+ (c^2+2\lambda_a)R^2-2cR+1\geqslant 0, $$ for a smooth axisymmetric Helfrich surfaces, that homeomorphic to a sphere, where $c$ is the spontaneous curvature of the surface, $\lambda_a$ and $\lambda_v$ are Lagrange multipliers, $R$ is the maximum distance between the axis of rotational symmetry and surface.
Keywords: Helfrich spheres of rotation, Willmore surface of rotation, Lobachevsky hyperbolic plane.
Mots-clés : Delaunay surface of rotation 
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     title = {On axisymmetric {Helfrich} surfaces},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {854--861},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a44/}
}
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S. M. Cherosova; D. A. Nogovitsyn; E. I. Shamaev. On axisymmetric Helfrich surfaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 854-861. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a44/