Proceedings of the Japan Academy, Series A, Mathematical Sciences

An area minimizing scheme for anisotropic mean curvature flow

Tokuhiro Eto, Yoshikazu Giga, and Katsuyuki Ishii

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Abstract

We consider an area minimizing scheme for anisotropic mean curvature flow originally due to Chambolle (2004). We show the convergence of the scheme to anisotropic mean curvature flow in the sense of Hausdorff distance by the level set method provided that no fattening occurs.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 1 (2012), 7-10.

Dates
First available in Project Euclid: 30 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.pja/1325264389

Digital Object Identifier
doi:10.3792/pjaa.88.7

Mathematical Reviews number (MathSciNet)
MR2872208

Zentralblatt MATH identifier
1275.35014

Subjects
Primary: 35D40: Viscosity solutions 35K65: Degenerate parabolic equations 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)
Secondary: 35K65: Degenerate parabolic equations 35K67: Singular parabolic equations

Keywords
Anisotropic mean curvature flow approximation scheme area minimization viscosity solutions

Citation

Eto, Tokuhiro; Giga, Yoshikazu; Ishii, Katsuyuki. An area minimizing scheme for anisotropic mean curvature flow. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 1, 7--10. doi:10.3792/pjaa.88.7. https://projecteuclid.org/euclid.pja/1325264389


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References

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