Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592469 | Journal of Functional Analysis | 2009 | 33 Pages |
Abstract
We provide a probabilistic approach to studying minimal surfaces in R3. After 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 minimal surface theory, maximum principle-type results, such as weak and strong halfspace theorems and the maximum principle at infinity, and Liouville theorems.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory