Displaying similar documents to “Singularity structure in mean curvature flow of mean-convex sets.”

A survey on Inverse mean curvature flow in ROSSes

Giuseppe Pipoli (2017)

Complex Manifolds

Similarity:

In this survey we discuss the evolution by inverse mean curvature flow of star-shaped mean convex hypersurfaces in non-compact rank one symmetric spaces. We show similarities and differences between the case considered, with particular attention to how the geometry of the ambient manifolds influences the behaviour of the evolution. Moreover we try, when possible, to give an unified approach to the results present in literature.

Anisotropic mean curvature on facets and relations with capillarity

Stefano Amato, Giovanni Bellettini, Lucia Tealdi (2015)

Geometric Flows

Similarity:

Given an anisotropy ɸ on R3, we discuss the relations between the ɸ-calibrability of a facet F ⊂ ∂E of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet ̃︀ BFɸ of the unit ball of ɸ, ɸ-calibrability is equivalent to show the existence of a ɸ-subunitary vector field in F, with suitable normal trace on @F, and with constant divergence equal to the ɸ-mean curvature of F. Assuming E convex at F, ̃︀ BFɸ a disk, and F (strictly) ɸ-calibrable,...

Type-II singularities of two-convex immersed mean curvature flow

Theodora Bourni, Mat Langford (2016)

Geometric Flows

Similarity:

We show that any strictly mean convex translator of dimension n ≥ 3 which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a consequence, we deduce that any translating solution of the mean curvature flow which arises as a blow-up limit of a two-convex mean curvature flow of compact immersed hypersurfaces of dimension n ≥ 3 is rotationally symmetric. The proof is rather robust, and applies to a more general class of translator equations....