The size of the singular set in mean curvature flow of mean-convex sets

White, Brian ¹

¹ Department of Mathematics, Stanford University, Stanford, California 94305

Journal of the American Mathematical Society, Tome 13 (2000) no. 3, pp. 665-695

Résumé

We prove that when a compact mean-convex subset of $\mathbf {R}^{n+1}$ (or of an $(n+1)$-dimensional riemannian manifold) moves by mean-curvature, the spacetime singular set has parabolic hausdorff dimension at most $n-1$. Examples show that this is optimal. We also show that, as $t\to \infty$, the surface converges to a compact stable minimal hypersurface whose singular set has dimension at most $n - 7$. If $n 7$, the convergence is everywhere smooth and hence after some time $T$, the moving surface has no singularities

Détail

DOI : 10.1090/S0894-0347-00-00338-6

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