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arXiv · 0805.0556

A martingale approach to minimal surfaces

Robert W. Neel
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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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Robert W. Neel. 2008-06-18. A martingale approach to minimal surfaces. https://doi.org/10.1016/j.jfa.2008.06.033

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