[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b200594

ALMOST RIGIDITY OF CONVEX HYPERSURFACES VIA THE EXTINCTION TIME OF MEAN CURVATURE FLOW

Huang, Xian-Tao (School of Mathematics Sun Yat-sen University)

Publication Information

Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 877-884 More about this Journal

Abstract

We prove that if a compact convex hypersurface of ℝⁿ⁺¹ has almost maximal extinction time when it is evolved by the mean curvature flow, then it must be nearly round in the C⁰-norm.

Keywords

Convex hypersurface; mean curvature flow; almost rigidity;

Citations & Related Records

Reference

1	R. H. Bamler and D. Maximo, Almost-rigidity and the extinction time of positively curved Ricci flows, Math. Ann. 369 (2017), no. 1-2, 899-911. https://doi.org/10.1007/s00208-016-1494-y DOI
2	T. H. Colding, Shape of manifolds with positive Ricci curvature, Invent. Math. 124 (1996), no. 1-3, 175-191. https://doi.org/10.1007/s002220050049 DOI
3	J. Cheeger and T. H. Colding, Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann. of Math. (2) 144 (1996), no. 1, 189-237. https://doi.org/10.2307/2118589 DOI
4	K. Ecker and G. Huisken, Interior estimates for hypersurfaces moving by mean curvature, Invent. Math. 105 (1991), no. 3, 547-569. https://doi.org/10.1007/BF01232278 DOI
5	R. S. Hamilton, Harnack estimate for the mean curvature flow, J. Differential Geom. 41 (1995), no. 1, 215-226. http://projecteuclid.org/euclid.jdg/1214456010 DOI
6	G. Huisken, Flow by mean curvature of convex surfaces into spheres, J. Differential Geom. 20 (1984), no. 1, 237-266. http://projecteuclid.org/euclid.jdg/1214438998 DOI
7	J. Langer, A compactness theorem for surfaces with L_p-bounded second fundamental form, Math. Ann. 270 (1985), no. 2, 223-234. https://doi.org/10.1007/BF01456183 DOI