no. 6
Codimension two surfaces pinched by normal curvature evolving by mean curvature flow
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 6, pp. 1599-1610.

We prove that codimension two surfaces satisfying a nonlinear curvature condition depending on normal curvature smoothly evolve by mean curvature flow to round points.

DOI : 10.1016/j.anihpc.2016.10.010
Mots clés : Curvature flow, Mean curvature, Nonlinear parabolic equations 
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     title = {Codimension two surfaces pinched by normal curvature evolving by mean curvature flow},
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     pages = {1599--1610},
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Baker, Charles; Nguyen, Huy The. Codimension two surfaces pinched by normal curvature evolving by mean curvature flow. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 6, pp. 1599-1610. doi : 10.1016/j.anihpc.2016.10.010. http://www.numdam.org/articles/10.1016/j.anihpc.2016.10.010/

[1] Andrews, Ben; Baker, Charles Mean curvature flow of pinched submanifolds to spheres, J. Differ. Geom., Volume 85 (2010) no. 3, pp. 357–395 MR2739807 (2012a:53122) | MR | Zbl

[2] Charles Baker, The mean curvature flow of submanifolds of high codimension, preprint, 2011.

[3] Chern, S.S.; do Carmo, M.; Kobayashi, S. Functional Analysis and Related Fields, Proc. Conf. for M. Stone, Springer, New York (1970), pp. 59–75 (Univ. Chicago, Chicago, Ill., 1968 MR0273546) | MR | Zbl

[4] Hamilton, Richard S. Three-manifolds with positive Ricci curvature, J. Differ. Geom., Volume 17 (1982) no. 2, pp. 255–306 MR664497 (84a:53050) | MR | Zbl

[5] Huisken, Gerhard Flow by mean curvature of convex surfaces into spheres, J. Differ. Geom., Volume 20 (1984) no. 1, pp. 237–266 MR772132 (86j:53097) | MR | Zbl

[6] Huisken, Gerhard Deforming hypersurfaces of the sphere by their mean curvature, Math. Z., Volume 195 (1987) no. 2, pp. 205–219 MR892052 (88d:53058) | MR | Zbl

[7] Smyth, Brian Submanifolds of constant mean curvature, Math. Ann., Volume 205 (1973) no. 4, pp. 265–280 | MR | Zbl

[8] Spivak, Michael A Comprehensive Introduction to Differential Geometry, vol. II, Publish or Perish, Inc., Wilmington, Del., 1979 MR532831 (82g:53003b) | MR | Zbl

[9] Topping, Peter Lectures on the Ricci Flow, London Mathematical Society Lecture Note Series, vol. 325, Cambridge University Press, Cambridge, 2006 MR2265040 (2007h:53105) | DOI | MR | Zbl

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