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Willmore minimizers with prescribed isoperimetric ratio. (English) Zbl 1288.74027
Summary: Motivated by a simple model for elastic cell membranes, we minimize the Willmore functional among two-dimensional spheres embedded in \({\mathbb R^3}\) with prescribed isoperimetric ratio.

74G65 Energy minimization in equilibrium problems in solid mechanics
74K15 Membranes
49Q10 Optimization of shapes other than minimal surfaces
52A40 Inequalities and extremum problems involving convexity in convex geometry
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