Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

Alex Freire

Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions

Analysis of PDEs 2008-09-04 v1 Differential Geometry

Authors: Alex Freire

Abstract

We consider a system of three surfaces, graphs over a bounded domain in ${\mathbb R}^2$ , intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to $2\pi/3$ .) For the corresponding two-dimensional parabolic free boundary problem we prove short-time existence of classical solutions (in parabolic H\"{o}lder spaces), for sufficiently regular initial data satisfying a compatibility condition.

Keywords

mean curvature motion triple junctions free boundary problem parabolic Hölder spaces short-time existence graphs

Cite

@article{arxiv.0809.0636,
  title  = {Mean Curvature Motion of Triple Junctions of Graphs in Two Dimensions},
  author = {Alex Freire},
  journal= {arXiv preprint arXiv:0809.0636},
  year   = {2008}
}