Existence and Regularity of Spheres Minimising the Canham–Helfrich Energy
Andrea Mondino, Christian Scharrer
Abstract
Abstract We prove the existence and regularity of minimisers for the Canham–Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the 2-sphere. This solves (the spherical case) of the minimisation problem proposed by Helfrich in 1973, modelling lipid bilayer membranes. On the way to proving the main results we establish the lower semicontinuity of the Canham–Helfrich energy under weak convergence of (possibly branched and bubbled) weak immersions.
Topics & Concepts
MathematicsSPHERESConvergence (economics)Minimisation (clinical trials)Mathematical analysisWeak convergenceEnergy (signal processing)Weak solutionClassical mechanicsComplex systemTotal energyBilayerClass (philosophy)Pure mathematicsContinuum hypothesisPhysicsExistence theoremUniform boundednessEnergy minimizationWeak formulationStored energyEnergy functionalMathematical Biology Tumor GrowthLipid Membrane Structure and BehaviorCell Adhesion Molecules Research