Introduction to mean curvature flow
Alessandroni, Roberta1
1 Albert-Einstein-Institut Max-Planck-Institut für Gravitationsphysik Am Mühlenberg 1 14476 Golm (Germany)
Séminaire de théorie spectrale et géométrie, Tome 27 (2008-2009), pp. 1-9.

This is a short overview on the most classical results on mean curvature flow as a flow of smooth hypersurfaces. First of all we define the mean curvature flow as a quasilinear parabolic equation and give some easy examples of evolution. Then we consider the M.C.F. on convex surfaces and sketch the proof of the convergence to a round point. Some interesting results on the M.C.F. for entire graphs are also mentioned. In particular when we consider the case of dimension one, we can compute the equation for the translating graph solution to the curve shortening flow and solve it directly.

DOI : 10.5802/tsg.267
Classification : 53C44
Mots clés : mean curvature flow, curve shortening flow, mean curvature flow for graphs
Alessandroni, Roberta 1

1 Albert-Einstein-Institut Max-Planck-Institut für Gravitationsphysik Am Mühlenberg 1 14476 Golm (Germany) 
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Alessandroni, Roberta. Introduction to mean curvature flow. Séminaire de théorie spectrale et géométrie, Tome 27 (2008-2009), pp. 1-9. doi : 10.5802/tsg.267. http://archive.numdam.org/articles/10.5802/tsg.267/

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