Bounding dimension of ambient space by density for mean curvature flow
Abstract
For an ancient solution of the mean curvature flow, we show that each time slice Mt is contained in an affine subspace with dimension bounded in terms of the density and the dimension of the evolving submanifold. Recall that an ancient solution is a family Mt that evolves under mean curvature flow for all negative time t.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.