Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation
Abstract
For any , let denote the space containing all locally Lipschitz minimal graphs of dimension and of arbitrary codimension in Euclidean space with uniformly bounded 2-dilation of their graphic functions. In this paper, we show that this is a natural class to extend structural results known for codimension one. In particular, we prove that any tangent cone of at infinity has multiplicity one. This enables us to get a Neumann-Poincar inequality on stationary indecomposable components of . A corollary is a Liouville theorem for . For small (we can take any ), we prove that (i) for , is flat; (2) for and a non-flat , any tangent cone of at infinity is a multiplicity one quasi-cylindrical minimal cone in whose singular set has dimension .
Cite
@article{arxiv.2109.09383,
title = {Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation},
author = {Qi Ding and J. Jost and Y. L. Xin},
journal= {arXiv preprint arXiv:2109.09383},
year = {2021}
}
Comments
56 pages