The gradient flow associated to the Helfrich variational problem, called the Helfrich flow is considered. Here the n-dimensional Helfrich flow is investigated for any n, as a projected gradient flow. A result of local existence is proved. The uniqueness is shown for the cases (i) for the initial hypersurface with non-zero Gramian when n ≥ 2, (ii) for every initial curve when n = 1.
"Local existence and uniqueness for the n-dimensional Helfrich flow as a projected gradient flow." Hokkaido Math. J. 41 (2) 209 - 226, June 2012. https://doi.org/10.14492/hokmj/1340714413