Global solutions to the volume-preserving mean-curvature flow

Luca Mugnai, Christian Seis, and Emanuele Spadaro

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Submission date: 26. Feb. 2015
Pages: 26
published in: Calculus of variations and partial differential equations, 55 (2016) 1, art-no. 18 
DOI number (of the published article): 10.1007/s00526-015-0943-x
Bibtex
MSC-Numbers: 53C44, 58E12, 65M06
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Abstract:
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 Almgren, Taylor and Wang (SIAM J. Control Optim. 31(2): 387- 438, 1993) and Luckhaus and Sturzenhecker (Calc. Var. Partial Differential Equations 3(2): 253-271, 1995).