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.
Mots clés : mean curvature flow, curve shortening flow, mean curvature flow for graphs
@article{TSG_2008-2009__27__1_0, author = {Alessandroni, Roberta}, title = {Introduction to mean curvature flow}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {1--9}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {27}, year = {2008-2009}, doi = {10.5802/tsg.267}, mrnumber = {2799143}, language = {en}, url = {http://www.numdam.org/articles/10.5802/tsg.267/} }
TY - JOUR AU - Alessandroni, Roberta TI - Introduction to mean curvature flow JO - Séminaire de théorie spectrale et géométrie PY - 2008-2009 SP - 1 EP - 9 VL - 27 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/tsg.267/ DO - 10.5802/tsg.267 LA - en ID - TSG_2008-2009__27__1_0 ER -
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://www.numdam.org/articles/10.5802/tsg.267/
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