Hokkaido Mathematical Journal

Local existence and uniqueness for the n-dimensional Helfrich flow as a projected gradient flow

Takeyuki NAGASAWA and Taekyung YI

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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.

Article information

Source
Hokkaido Math. J. Volume 41, Number 2 (2012), 209-226.

Dates
First available in Project Euclid: 26 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1340714413

Digital Object Identifier
doi:10.14492/hokmj/1340714413

Mathematical Reviews number (MathSciNet)
MR2977045

Zentralblatt MATH identifier
1247.53083

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 49Q10: Optimization of shapes other than minimal surfaces [See also 90C90] 53A04: Curves in Euclidean space 53A05: Surfaces in Euclidean space 58J35: Heat and other parabolic equation methods 35K30: Initial value problems for higher-order parabolic equations

Keywords
Helfrich variational problem gradient flow constraints

Citation

NAGASAWA, Takeyuki; YI, Taekyung. Local existence and uniqueness for the n -dimensional Helfrich flow as a projected gradient flow. Hokkaido Math. J. 41 (2012), no. 2, 209--226. doi:10.14492/hokmj/1340714413. https://projecteuclid.org/euclid.hokmj/1340714413.


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