NAGASAWA Takeyuki, YI Taekyung,
Local existence and uniqueness for the n-dimensional Helfrich flow as a projected gradient flow.
Hokkaido Mathematical Journal, 41 (2012) pp.209-226
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.
|MSC(Secondary)||49Q10, 53A04, 53A05, 58J35, 35K30|
|Uncontrolled Keywords||Helfrich variational problem, gradient flow, constraints|