We show that local minimizers of the Canham–Helfrich energy are asymptotically stable with respect to a model for relaxational fluid vesicle dynamics that we already studied in previous papers ([13, 14]). The proof is based on a Łojasiewicz–Simon inequality.
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Daniel Lengeler, Asymptotic stability of local Helfrich minimizers. Interfaces Free Bound. 20 (2018), no. 4, pp. 533–550DOI 10.4171/IFB/411