## 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

### Fulltext

PDF### Abstract

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(Primary) | 53C44 |
---|---|

MSC(Secondary) | 49Q10, 53A04, 53A05, 58J35, 35K30 |

Uncontrolled Keywords | Helfrich variational problem, gradient flow, constraints |