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A martingale approach to minimal surfaces

Authors
  • Neel, Robert W.
Type
Published Article
Publication Date
Jun 18, 2008
Submission Date
May 05, 2008
Identifiers
DOI: 10.1016/j.jfa.2008.06.033
Source
arXiv
License
Yellow
External links

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.

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