Global solutions to the volume-preserving mean-curvature flow. (English) Zbl 1336.53082
Summary: In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by F. Almgren et al. [SIAM J. Control Optim. 31, No. 2, 387–438 (1993; Zbl 0783.35002)] and S. Luckhaus and T. Sturzenhecker [Calc. Var. Partial Differ. Equ. 3, No. 2, 253–271 (1995; Zbl 0821.35003)].
MSC:
| 53C44 | Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) |
| 58E12 | Variational problems concerning minimal surfaces (problems in two independent variables) |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
mean-curvature flow; volume preserving; volume constraint; global solutions; time discretizationReferences:
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