Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type
نویسندگان
چکیده
منابع مشابه
The Nature of Singularities in Mean Curvature Flow of Mean-convex Sets
Let K be a compact subset of R, or, more generally, of an (n+1)-dimensional riemannian manifold. We suppose that K is mean-convex. If the boundary of K is smooth and connected, this means that the mean curvature of ∂K is everywhere nonnegative (with respect to the inward unit normal) and is not identically 0. More generally, it means that Ft(K) is contained in the interior of K for t > 0, where...
متن کاملSingularity Structure in Mean Curvature Flow of Mean Convex Sets
In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres. In this note we announce results on the mean curvature flow of mean convex sets; all the statements below have ...
متن کاملMarangoni-driven singularities via mean-curvature flow
In this work, it is demonstrated that the existence and topology of the recently observed interfacial singularities driven by Marangoni effects can be deduced using mean-curvature flow theory extended to account for variations of interfacial tension. This suggests that some of the physical mechanisms underlying the formation of these interfacial singularities may originate from/be modeled by th...
متن کاملCrystalline mean curvature flow of convex sets
We prove a local existence and uniqueness result of crystalline mean curvature flow starting from a compact convex admissible set in R . This theorem can handle the facet breaking/bending phenomena, and can be generalized to any anisotropic mean curvature flow. The method provides also a generalized geometric evolution starting from any compact convex set, existing up to the extinction time, sa...
متن کاملNon-collapsing in Mean-convex Mean Curvature Flow
We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence. We follow [4] in defi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2019
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.21852