An inscribed radius estimate for mean curvature flow in Riemannian manifolds

2013/10/13 by Brendle, S.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1310.3439

Abstract

We consider a family of embedded, mean convex hypersurfaces in a Riemannian manifold which evolve by the mean curvature flow. We show that, given any number T>0 and any δ>0, we can find a constant C₀ with the following property: if t ∈ [0,T) and p is a point on M_t where the curvature is greater than C₀, then the inscribed radius is at least (1)/((1+δ) H) at the point p. The constant C₀ depends only on δ, T, and the initial data.

Related

• On Brendle's estimate for the inscribed radius under mean curvature flow
• Mean curvature flow with surgery of mean convex surfaces in ℝ³
• A sharp inscribed radius estimate for fully nonlinear flows
• Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4
• On the extension to mean curvature flow in lower dimension