Uniform ball property and existence of optimal shapes for a wide class of geometric functionals

DOI10.4171/IFB/401zbMath1397.49057arXiv1504.04189OpenAlexW2963883137MaRDI QIDQ1655861

Jérémy Dalphin

Publication date: 10 August 2018

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1504.04189

zbMATH Keywords

shape optimizationWillmore functionalgeometric functionalsCanham-Helfrich energycurvature depending energiesuniform ball condition

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05)

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Optimal shape of stellarators for magnetic confinement fusion ⋮ Total positive curvature and the equality case in the relative isoperimetric inequality outside convex domains ⋮ Existence and regularity of spheres minimising the Canham-Helfrich energy ⋮ The weighted Hardy constant ⋮ Existence of optimal shapes under a uniform ball condition for geometric functionals involving boundary value problems

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