带三重边的平均曲率流的局部正则性定理
微分几何
2017-06-07 v2 偏微分方程分析
摘要
R^{n+k}中n维曲面簇的平均曲率流沿光滑边以相等角度三重相交并在低维面上具有高阶结点，是经典平均曲率流的自然推广。我们称此类流为带三重边的平均曲率流。我们证明，若光滑带三重边的平均曲率流弱接近于三个n维单位密度半平面的静态并集，则它光滑接近。将正则性结果推广到一类整数Brakke流，我们表明这蕴含从具有三重边但无高阶结点的初始曲面簇出发的流的光滑短时间存在性。
引用
@article{arxiv.1605.06592,
title = {A local regularity theorem for mean curvature flow with triple edges},
author = {Felix Schulze and Brian White},
journal= {arXiv preprint arXiv:1605.06592},
year = {2017}
}
备注
Existence proof extended to cover existence of a Brakke flow, starting from a general cluster in arbitrary codimension. Added details in proof of initial smoothness. Presentation improved, references updated, some typos fixed. 25 pages