Search
Talk

On the mean curvature flow of grain boundaries

  • Yoshihiro Tonegawa (Tokyo Institute of Technology)
A3 01 (Sophus-Lie room)

Abstract

Suppose that C in n+1-dimensional Euclidean space is a closed countably n-rectifiable set whose complement consists of more than one connected component. Assume that the n-dimensional Hausdorff measure of C is finite or grows at most exponentially near infinity, but no further regularity is assumed. Examples of C are planar networks in 2D, soap bubble clusters in 3D, and co-dimension one simplicial complexes in general dimensions. Very recently, we have proved a global-in-time existence of nontrivial mean curvature flow in the sense of Brakke starting from C. There exists a finite family of open sets which move continuously with respect to the Lebesgue measure, and whose boundaries coincide with the space-time support of the mean curvature flow. One may consider the open sets as grains and the flow as the mean curvature flow of grain boundaries. In this talk, mainly the background and results are discussed and if time permits, some key concepts will be discussed. This is a joint work with Lami Kim.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss