A generalization of Rado's Theorem for almost graphical boundaries
Differential Geometry
2007-05-23 v1
Abstract
In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is "almost graphical" in some sense, that the surface must be graphical once we move sufficiently far from the boundary.
Keywords
Cite
@article{arxiv.math/0502551,
title = {A generalization of Rado's Theorem for almost graphical boundaries},
author = {Brian Dean and Giuseppe Tinaglia},
journal= {arXiv preprint arXiv:math/0502551},
year = {2007}
}
Comments
12 pages, 6 figures, submitted to Math. Zeit