A martingale approach to minimal surfaces
Differential Geometry
2011-01-20 v2 Probability
Abstract
We provide a probabilistic approach to studying minimal surfaces in three-dimensional Euclidean space. Following a discussion of the basic relationship between Brownian motion on a surface and minimality of the surface, we introduce a way of coupling Brownian motions on two minimal surfaces. This coupling is then used to study two classes of results in the theory of minimal surfaces, maximum principle-type results, such as weak and strong halfspace theorems and the maximum principle at infinity, and Liouville theorems.
Cite
@article{arxiv.0805.0556,
title = {A martingale approach to minimal surfaces},
author = {Robert W. Neel},
journal= {arXiv preprint arXiv:0805.0556},
year = {2011}
}
Comments
33 pages, exposition in Section 3 re-worked, minor corrections, one reference added