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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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.

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

First available in Project Euclid: 30 December 2011

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Zentralblatt MATH identifier

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

Anisotropic mean curvature flow approximation scheme area minimization viscosity solutions


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.

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